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General Physics
Objective Question
Q.1
The fundamental unit which has same power in the dimensional formula of surface tension and viscosity is :
(a)
Q.2
Q.3
Mass
(b)
Length
(c)
(d)
None
Indicate which pairs of physical quantities given below has not the same units and dimensions :
(a)
Momentum and impulse
(b)
Torque and angular momentum
(c)
Acceleration and gravitational field strength
(d)
Pressure and modulus of elasticity
The dimensions of pressure are :
(a)
[MLT-2]
(b)
[ML-1T2]
[ML-1T-2]
(d)
[MLT2]
[M L-1 T--2]
(d)
[ML-2 T-2]
(c)
[MLT-1]
(d)
[ML2T-2]
(c)
Frequency
[ML-1T-2]
(d)
[MLT-2]
[M-1L3T-2]
(d)
[M-1LT-2]
(c)
Q.4
The dimensions of torque are :
Q.5
(a)
[M L2 T-2]
(b)
[M L T-2]
(c)
The dimensional formula for angular momentum is :
(a)
Q.6
Time
[M0L2T-2]
(b)
[ML2T-1]
Planck’s constant has the dimensions of :
(a)
Energy
(b)
(d)
Angular momentum
Momentum
Q.7
The dimensional formula for Planck’s constant is :
Q.8
(a)
[ML2T-1]
(b)
[ML2T3]
(c)
The dimensions of gravitational constant G are :
(a)
[MLT-2]
(b)
[ML3T-2]
(c)
Q.9
The dimensional formula for modulus of rigidity is :
Q.10
(a)
[ML-1T-1]
(b)
[ML-2T2]
(c)
[MLT-1] (d)
[ML-1T-2]
Turpentine oil is flowing through a tube of length l and radius r. The pressure difference between the two ends
of the tube is p; the viscosity of the oil is given by :
 = p (r2 – x2)/4l
where v is the velocity of oil at a distance x from the axis of the tube. From this relation, the
dimensions of viscosity  are :
Q.11
(a)
[M0L0T0]
(b)
[MLT-1]
(c)
[ML2T-2]
(d)
[ML-1T-1]
The velocity  of a point at time t is given by :
 = at + b/ (t + c)
The dimensions of a, b and c are respectively :
Q.12
(a)
L2; T and LT2
(b)
LT2; LT and L
(c)
LT-2; L and T
(d)
L; LT and T2
The time dependence of a physical quantity p is given by P = P0 exp (-t2) [where  is a constant and t is time].
The constant :
(a)
is dimensions [T2]
is dimensions
(d)
(b)
has dimensions [T-2]
is dimensions of p
(c)
Q.13
Q.14
Q.15
Q.16
Q.17
Q.18
Q.19
Q.20
Q.21
Q.22
Q.23
Q.24
Q.25
Q.26
The velocity of water waves may depends on their wavelength , the density of water  and the acceleration due
to gravity g. The method of dimensions gives the relation between these quantities as :
(a)
V2  g-1 -1
(b)
V2  g
(c)
V2  g
(d)
V2  g-1 -3
The time period T of a small drop of liquid (due to surface tension) depends on density , radius r and surface
tension S. The relation is :
(a)
T  (r3/S)1/2
(b)
T  rS
(c)
T  r/S
(d)
T  (S/r)
P represents radiation pressure, c represents speed of light and S represents radiation energy striking unit area
per sec. The non zero integers x, y and z such that PxSycz is dimensionless are :
(a)
x = 1, y =1, z = 1
(b)
x = -1, y =1, z = 1
(c)
x = 1, y =-1, z = 1
(d)
x = 1, y =1, z = 1
The measured mass and volume of a body are 23.42 g and 4.9 cm3 respectively with possible error 0.01 g and
0.1 cm3. The maximum error in density is nearly
(a)
0.2%
(b)
2%
(c)
5%
(d)
10%
The least count of a stop watch is 0.2 second. The time of 20 oscillations of a pendulum is measured to be 25
second. The percentage error in the measurement of time will be
(a)
8%
(b)
1.8%
(c)
0.8% (d)
0.1%
A student measures quantities a,b and c and then calculates S by the formula S = ab 2/c3. If the errors in a,b,c are
1%, 3% and 2% respectively, the maximum error in S can be :
(a)
13%
(b)
7%
(c)
4%
(d)
1%
The percentage errors in the measurement of mass and length of the edge of a cube are 3% and 2% respectively.
The maximum percentage errors in the density would be :
(a)
1%
(b)
5%
(c)
9%
(d)
11%
The pressure on a square plate is measured by measuring the force on the plate and the length of the side of the
plate. The errors in the measurement of force and length are 4% and 2% respectively. The maximum error in the
value of the pressure would be
(a)
1%
(b)
2%
(c)
6%
(d)
8%
Four persons measure the thickness of a paper and express it in the following way. Which measurement is
maximum accurate?
(a)
3.00  10-4 m
(b)
30  10-3 cm
-2
(c)
3  10 cm
(d)
0.030 cm.
The length and breadth of a metal sheet are 3.124m and 3.002 m respectively. The area of this sheet up to four
correct significant figures is
(a)
9.3m2
(b)
9.378m2
(c)
9.3782m2
(d)
9.378248m2.
Which of the following measurements is most significant?
(a)
0.003 mm
(b)
3.00 mm
(c)
30.00 mm
(d)
3.0 mm
A vectors A points vertically upwards and B points toward north. The vectors produced A  B is :
(a)
along west
(b)
along east
(c)
zero
(d)
vertically downwards
Which of the following physical quantities are represented by polar vectors?
(a)
Displacement
(b)
Angular Velocity
(c)
Angular momentum
(d)
Torque
The flight of a bird can be example of :
(a)
dot product of vectors
(b)
cross product of vectors
(c)
composition of vectors
(d)
Triangle law of vector addition
Q.27
The vectors A and B are such that A + B = A – B then the angle between the two vectors A and B will be
(a)
Q.28
0
 = 0
(c)
90
(d)
180
(b)
 = /2 (c)
 = 2/3
=
(d)
A + B = C, the angle between A and B is 120 and A = B. If A + B + C = 0. Then what is the angle between A
and B?
(a)
Q.30
60
Two vectors A and B are such that A + B = C and A2 + B2 = C2. If  is the angle between positive directions A
and B then mark the correct alternative :
(a)
Q.29
(b)
30
(b)
60
(c)
120
(d)
150
If | P | = | Q | and the angle between P and Q is neither 0 nor 180, then what is the angle between P + Q and
P – Q?
(a)
0
(b)
30
(c)
60
(d)
90
Answer Sheet
General Physics
1.
(a)
2.
(c)
3.
(c)
4
(a)
5.
(d)
6.
(a)
7.
(c)
8.
(d)
9.
(d)
10.
(c)
11.
(b)
12.
(b)
13.
(a)
14.
(c)
15.
(a)
16
(b)
17.
(c)
18.
(a)
19.
(c)
20.
(d)
21.
(a)
22.
(b)
23.
(c)
24.
(a)
25.
(a)
26.
(c)
27.
(c)
28.
(b)
29.
(c)
30.
(b)
Kinematics
DISTANCE, DISPLACEMENT AND VELOCITY,ACCLERATED MOTION
Q.1
Q.2
Q. 3
Q.4
Q.5
Q.6
A ball is thrown vertically upwards from the ground G with a speed u. It reaches a point B at a height h (lower
than the maximum height) after time t1. It return to the ground after time t2 from the instant it was at B during the
upward journey. Then t1t2 is equal to :
(a)
2h/g
(b)
h/g
(c)
h/2g
(d)
h/4g
A ball is dropped from the top of the tower of height h. It covers a distance of h/2 in the last second of its motion.
How long does the ball remain in air? (Take g = 10 ms-2)
(a)
2s
(b)
(2 2)s
(c)
2s
(d)
none of these
A bus is moving with a velocity 10 ms-1 on a straight road. A scooterist wishes to cover-take the bus in 100 s. If
the bust is a distance of 1 km from the scooterist, with what velocity should the scooterist chase the bus?
(a)
50 ms-1
(b)
40 ms-1
(c)
30 ms-1
(d)
20 ms-1
A car is moving eastwards with velocity 10 m/s. In 20 sec, the velocity changes to 10 m/s northwards. The
average acceleration in this time :
(a)
1/2 ms-2 towards N-W
(b)
1/2 ms-2 towards N-E
(c)
½ ms-2 towards N-W
(d)
½ ms-2 towards N-E
2
A body starts from rest with a uniform acceleration of 2 m/s for 10 sec, it moves with constant speed for 30 sec
then decelerates by 4 m/s2 to zero. What is the distance covered by the body?
(a)
750 m
(b)
850 m
(c)
600 m
(d)
none of these
A body dropped from a height h with an initial speed zero reaches the ground with a velocity of 3 km/h. Another
body of the same mass was dropped from the same height h with an initial speed 4 km/h, will reach the ground
with a velocity of :
(a)
3 km/h
(b)
4 km/h
(c)
5 km/h
(d)
12 km/h
Q.7
Q.8
Q.9
Q.10
Q.11
Q.12
Q.13
Q.14
Q.15
Q.16
Q.17
Q.18
Q.19
Q.20
Q.21
Q.22
Q.23
A parachutist after bailing out falls 50 m without friction when parachute opens, it decelerates at 2 m/s 2. He
reaches the ground with a speed of 3 m/s. At what height, did he bail out?
(a)
293 m
(b)
111m
(c)
91 m
(d)
182 m
A car covers 1/3 distance with speed 20 km/hr and 2/3 with 60 km/hr. Average speed is :
(a)
40 km/hr
(b)
502 km/hr
(c)
36 km/hr
(d)
48 km/hr.
A particle is thrown vertically upwards. Find the velocity so that it covers same distance in 5 th and 6th seconds :
(a)
48 m/s
(b)
14 m/s
(c)
49 m/s
(d)
7 m/s.
From the top of a tower, a particle is thrown vertically downwards with a velocity of 10 m/s. The ratio of the
distance covered by it in the 3rd and 2nd seconds of the motion is :
(a)
5:7
(b)
7:5
(c)
3:6
(d)
6 : 3.
A ball is thrown from height h and another from 2h. The ratio of time taken by the two balls to reach ground is :
(a)
1: 2
(b)
2 : 1
(c)
2:1
(d)
1 : 2.
Two bodies A (off mass 1 kg) and B (of mass 3 kg) are dropped from height of 16 m and 25 m respectively. The
ratio of the time taken by them to reach the ground is :
(a)
4/5
(b)
5/4
(c)
12/5
(d)
5/12.
A particle is moving eastwards in a velocity of 5m s-1. In 10 seconds the velocity changes to 5m s -1 northwards.
The average acceleration in this time is
(a)
zero
(b)
1/2 m s-2 towards north-west
-2
(c)
1/2 m s towards north-east (d)
½ m s-2 towards north.
A-Train covers one half of its journey between two stations with speed v1 and the remaining half with speed v2.
The average speed for the whole journey is
(a)
v1+v2/2
(b)
2 v1v2 / v1+v2
(c)
 v1v2
(d)
 v1/v2
A 150 m long train is moving north at a speed of 20m/s. A bird flying south at a speed of 5m/s cross the train.
What is the time taken by the bird to cross the train
(a)
30s
(b)
10s
(c)
7.5s
(d)
6s
From a 20 m high tower one ball is thrown upwards with speed of 10m/s and another is thrown vertically
downwards at the same speed simultaneously. The time difference of their reaching the ground will be
(Take
g = 10ms-2)
(a)
12s
(b)
6s
(c)
2s
(d)
1s
A particle is projected vertically upwards. It attains a height h after 2 seconds and again after 10 seconds. The
speed of the particle at the height h is numerically equal to
(a)
g
(b)
2g
(c)
4g
(d)
6g
Two objects begin free fall from rest from the same height with a time gap of 1s. How long after the first object
begins to fall will the two bodies be 10m apart.
(a)
3.5s
(b)
2s
(c)
0.5s
(d)
1.5s
If the speed of a truck is reduced to 1/3 of its original value, the minimum distance required to stop will be
(a)
same as before
(b)
1/3 of its original value
(c)
1/9 of its original value
(d)
2/3 of its original value
The magnitude of average velocity is equal to the average speed when a particle moves :
(a)
on a curved path
(b)
in the same direction
(c)
with constant acceleration
(d)
with constant retardation
If a particle moves with a constant velocity :
(a)
its acceleration is positive
(b)
its acceleration is negative
(c)
its acceleration is zero
(d)
its speed is zero
A particle moving in a straight line cover half the distance with speed of 3 m/s. the other half of the distance is
covered in two equal time intervals with speed of 4.5m/s and 7.5 m/s respectively. The average speed of the
particle during this motion is :
(a)
4 m/s
(b)
5 m/s
(c)
5.5 m/s
(d)
4.8 m/s
A ball is released from the top of a tower of height h meters. It takes T seconds to reach the ground. What is the
position of the ball at T/3 second ?
(a)
8h/9 meters from the ground
(b)
7h/9 meters from the ground
Q.24
Q.25
Q.26
Q.27
Q.28
Q.29
Q.30
(c)
h/9 meters from the ground
(d)
17h/18 meters from the ground
If a train traveling at 72 km/h is to be brought to rest in a distance of 200m, then its retardation should be :
(a)
20 m/s2
(b)
2 m/s2
(c)
10 m/s2
(d)
1 m/s2
A body travels 200 cm in the first two seconds and 220 cm in the next 4 sec with deceleration. The velocity of
the body at the end of the 7th second is :
(a)
5 cm/s
(b)
10 cm/s
(c)
15 cm/s
(d)
20 cm/s
A car moving with a speed of 40 km/hr, can be stopped by applying brakes after at least 2m. If the same car is
moving with a speed of 80 km/hr, what is the minimum stopping distance?
(a)
2m
(b)
4m
(c)
6m
(d)
8 m.
An electron of mass m e, initially at rest, moves through a certain distance in a uniform electric field in time t 1. A
proton of mass m p, also initially at rest, takes time t2 to move through an equal distance in this uniform electric
field. Neglecting the effect of gravity, the ration t2/t1 is nearly equal to :
(a)
1
(b)
(mp/me)1/2
(c)
(me/mp)1/2
(d)
1836
A particle is dropped vertically from rest, from a height. The time taken by it to fall through successive distance
of 1 km each will then be :
(a)
(b)
all equal, being equal to 2/g second
in the ratio of the square roots of the integers 1, 2 3, . . .
(c)
in the ratio of the difference in the square roots of the integers, i.e., 1, (2 - 1), (3 - 2), (4 3), . . .
(d)
in the ratio of the reciprocal of the square roots of the integers, i.e, 1/1 , 1/2 , 1/3 , . . .
An object accelerates from rest to a velocity 27.5 m/s in 10 sec, then find distance covered by next 10 sec:
(a)
550 m
(b)
137.5 m
(c)
412.5 m
(d)
275 m.
A body falls freely from rest. It covers as much distance in the last second of its motion as covered in the first
three second. The body has fallen for a time of :
(a)
3s
(b)
5s
(c)
7s
(d)
9s
Answer Sheet
DISTANCE, DISPLACEMENT AND VELOCITY,ACCLERATED MOTION
1.
(d)
2.
(b)
3.
(d)
4
(a)
5.
(a)
6.
(c)
7.
(a)
8.
(c)
9.
(c)
10.
(b)
11.
(c)
12.
(a)
13.
(b)
14.
(b)
15.
(d)
16
(c)
17.
(c)
18.
(d)
19.
(c)
20.
(b)
21.
(c)
22.
(a)
23.
(c)
24.
(d)
25.
(b)
26.
(d)
27.
(b)
28.
(c)
29.
(a)
30.
(b)
Graph & Problems on Integration and Differentiation
Q.1
Q.2
Q.3
Q.4
Q.5
Q.6
Q.7
Q.8
Q.9
Q.10
Q.11
Q.12
Q.13
Q.14
A particle moves along x-axis in such a way that its coordinate x varies with time t according to the expression
x = 2 – 5t + 6t2
The initial velocity of the particle is
(a)
- 5m/s
(b)
-3 m/s
(c)
3 m/s
(d)
6 m/s
A particle starts from rest and travels in a straight line with an acceleration which varies with time t as follows
a=6–2t
The distance traveled by the particle in 3s is
(a)
9m
(b)
12 m
(c)
15 m
(d)
18 m
A bird flies in straight line for 4s with a velocity  = (2t - 4) m/s. What is the distance covered by the bird in
returning to the place from where it started its journey?
(a)
0
(b)
8m
(c)
4m
(d)
2m
A particle starts from rest at the origin and moves along X-axis with acceleration
a = 12 – 2 t
The time after which the particle arrives at the origin is
(a)
6s
(b)
18 s
(c)
12 s
(d)
4s
The position x of a particle varies with time (t) as x = at2 – bt3. The acceleration at time t of the particle will be
equal to zero, where t is equal to :
(a)
2a/3b
(b)
a/b
(c)
a/3b
(d)
zero
The displacement s of a particle is proportional to the first power of time t, i.e., s  t, then the acceleration of the
particle is :
(a)
infinite
(b)
zero
(c)
a small finite value
(d)
a large finite value
The displacement s of a particle is proportional to the second power of time t, i.e., s  t2, then the initial velocity
of the particle is :
(a)
infinite
(b)
zero
(c)
positive finite value
(d)
negative finite value
The distance traveled by a particle is directly proportional to t 1/2, where t = time elapsed. What is the nature of
motion?
(a)
Increasing acceleration
(b)
Decreasing acceleration
(c)
Increasing retardation
(d)
Decreasing retardation
The displacement of a body is given by 4s = M + 2Nt4, where M and N are constants. The velocity of the body
at any instant is :
(a)
M + 2Nt4/4
(b)
2N
(c)
M + 2 N/4
(d)
2Nt3
The acceleration of particle, starting from rest, varies with time according to the relation :
A = -s2 sin t
The displacement of this particle at a time t will be :
(a)
s sin t
(b)
s cos t
(c)
s sin t(d)
½ (s2 sin t)t2
If x denotes displacement in time t and x = a cos t, then acceleration is :
(a)
a cos t
(b)
- a cos t
(c)
a sin t
(d)
-a sin t
The relation between time t and distance x is t = x2 + x where  and  are constants. The acceleration is :
(a)
-2v3
(b)
2v3
(c)
-2v3
(d)
The velocity time relation of an electron starting from rest is given by v = kt where k
traversed in 3 sec is :
(a)
9m
(b)
16 m
(c)
27 m
(d)
A particle moves along a straight line such that its displacement at any time t is given by
S = (t3 – 3t2 + 2)m
The displacement when the acceleration becomes zero is :
(a)
0m
(b)
2m
(c)
3m
(d)
23v3
= 2 m/s 2. The distance
36 m
-2 m
Q.15
Q.16
Q.17
Q.18
Q.19
Q.20
Q.21
Q.22
Q.23
Q.24
Q.25
A point moves in a straight line so that its displacement x m at time t sec is given by x2 = 1 + t2. Its acceleration
in m/sec2 at a time t sec is
(a)
1/x3
(b)
-t/x3
2 3
(c)
1/x – t /x
(d)
1/x – 1/x3
A body is moved along a straight line by a machine delivering constant power. The distance moved by the body
in time t is proportional to :
(a)
t1/2
(b)
t3/4
(c)
t3/2
(d)
t2
2
-bt
The displacement of a particle after time t is given by x = (k/b )(1 –e ), where b is a constant. What is the
acceleration of the particle?
(a)
ke-bt
(b)
-ke-bt
(c)
k/b2e-bt
(d)
-k/b2e-bt
2
The velocity v and displacement r of a body are related as v = kr, where k is a constant. What will be the
velocity after 1 second? Given that the displacement is zero at t = 0 :
(a)
k r
(b)
k r3/2
0
(c)
k/2r
(d)
data is not sufficient
A particle’s position as a function of time is described as y (t) = 2t 2 + 3t + 4. What is the average velocity of the
particle from t = 0 to t = 3 sec?
(a)
3 m/s
(b)
6 m/s
(c)
9 m/s
(d)
12 m/s
The displacement x of a particle moving in one dimension under the action of constant force is related to time t
by the equation t = x + 3, where x is in metres and t is in seconds. Find the displacement of the particle when
its velocity is zero.
(a)
zero
(b)
12 m
(c)
6m
(d)
18 m
A travelling wave in a stretched string is described by the equation y =A sin (kx -t)
The maximum particle
velocity is
(a)
A

b)
/k
(c)
ddt
(d)
x/t
The x and y coordinates of a particle at any time t are given by :
x = 7t + 4t2
and
y = 5t
Where x and y are in m and t in s. The acceleration of the particle at 5s is :
(a)
zero
(b)
8 m/s2
(c)
20 m/s2
(d)
40 m/s2
The position vector of a particle is given by r = r0 (1 - at)t, where t is the time and a as well as r0 are constants.
After what time the particle returns to the starting point ?
(a)
a

b)
1/a
(c)
a2
(d)
1/a2
The acceleration of a particle varies with time as a = bt + c, where b and c are constant. What will be the
velocity of the particle which starts from rest after the time t? 
(a)
bt + 1/2ct2
b)
ct + ½ bt2
(c)
bt + ct2
(d)
ct + bt2
A body is moving according to the equation :
x = at + bt2 – ct3
where x = displacement and a, b and c are constants. The acceleration of the body is :
(a)
a + 2bt 



b)
2b + 6ct
(c)
2b – 6ct
(d)
3b – 6ct2
Answer Sheet
1.
(a)
2.
(d)
3.
(b)
4
(b)
5.
(c)
6.
(b)
7.
(b)
8.
(d)
9.
(d)
10.
(a)
11.
(b)
12.
(a)
13.
(a)
14.
(a)
15.
(c)
16
(c)
17.
(b)
18.
(c)
19.
(c)
20.
(a)
21.
(a)
22.
(b)
23.
(b)
24.
(b)
25.
(c)
PROJECTILE MOTION
Q.1
Q.2
An object is thrown along a direction inclined at an angle of 45 with the horizontal. The horizontal range of the
particle is equal to
(a)
vertical height
(b)
twice the vertical height
(c)
thrice the vertical height
(d)
four the vertical height
The greatest distance to which a man can throw a stone is a. The greatest height to which he can throw it will be
(a)
a
(b)
a/2
(c)
2/ a
(d)
a/3
Q.3
Two bodies are projected from the same point with the same speed but in different directions so as to have the
same range. The ratio of their times of flight are
(a)
1:1
(b)
1: cos 
(c)
1: sin 
(d)
1: cot 
Q.4
The range of projectile which is launched at an angle of 15 with the horizontal is 1.5km. What is the range of
the projectile if it is projected at an angle of 45 to the horizontal?
(a)
1.5km
(b)
3.0km
(c)
6.0km
(d)
0.75km
Q.5
A man has two spheres A and B. He is standing at the top of a tower. He gently drops the sphere A vertically
downwards and throws the sphere B horizontally at the same time. Which of the following is the correct
statement?
(a)
both the sphere will reach the ground simultaneously
(b)
sphere A will reach the ground earlier
(c)
sphere B will reach the ground earlier
(d)
the question is incomplete because the masses of the sphere are not given
Q.6
The range of projectile is 24m and the maximum height reached is 8m. The initial velocity and angle of
projection are
(a)
6g , sin-1(0.8)
(b)
5g , sin-1(0.6)
-1
(c)
5g , sin (0.8)
(d)
4g , sin-1(0.6)
Q.7
A particle is projected with the speed of 105m/s at an angle of 60 from the horizontal, the velocity in m/s of
the projectile when it reaches the height of 10m is (Take g=9.8m/s)
(a)
419
(b)
179
(c)
15
(d)
515
*Q.8 A lift is moving vertically upwards. At the instant when its velocity is v and downward acceleration is a (<g), a
stone is projected from a point on its floor at an angle  with the horizontal. The trajectory of the stone is
(a)
a parabola in the lift frame
(b)
a parabola in the ground frame
(c)
a straight line in the lift frame
(d)
a straight line in the ground frame
Q.9
A particle is projected with a velocity of 19.6m/s at an angle of 30 with the horizontal. It will move at right
angles to its initial directions of motion after a time of
(a)
2s
(b)
6s
(c)
4s
(d)
8s
Q.10 A particle of mass m is projected from a point A at an angle of 45 with the horizontal with a speed v. If the time
taken to reach the highest point B is t, What is the change in its velocity from its departure at A to its arrival at
B?
(a)
2v
(b)
v/2
(c)
gt
(d)
½ gt2
Q.11 A projectile of mass m is fired with the velocity v from ground at an angle of 45 with horizontal. Neglecting air
resistance, the magnitude of change in momentum between leaving and arriving at the ground is
(a)
zero
(b)
½ mv
(c)
2 mv
(d)
2mv
Q.12 A shell is fired a cannon with a velocity v at an angle  with the horizontal direction. At the highest point in its
path it explodes into two pieces of equal mass. One of the pieces retraces its path to the canon and the speed of
the other piece immediately after the explosion is
(a)
3v cos 
(b)
2v cos
(c)
3/2 v cos 
(d)
3/2 v cos
Q.13 A body of mass 1kg is thrown from a point A with a velocity 20m/s at an angle 45 with the horizontal. If the
highest point attained by it is B, calculate the work done by the gravity during its journey from A to B. (g= take
10 m/s2)
(a)
200J
(b)
–200J
(c)
–100J
(d)
100J
Q.14 A body of mass 1kg is thrown with a velocity 40m/s at an angle of 30 with the horizontal. What is the change
in its momentum during the interval 1.0s to 3.0s (Take g = 10m,/s2)
(a)
–20kg ms-1
(b)
40kg ms-1
(c)
0
(d)
–40 kg ms-1
Q.15 A body of mass 1kg is thrown with a velocity of 40m/s at an angle of 30 with the horizontal. Calculate the
work done by the gravity during the interval of 1.0s to 3.0s (Take g = 10m,/s2)
(a)
800J
(b)
400J
(c)
–800J
(d)
0
*Q.16 In case of projectile motion of two projectiles A and B are projected with the same speed at angles 15 and 75
respectively to the horizontal, then
(a)
HA > HB
(b)
HA < HB
(c)
TA > TB
(d)
TA < TB
Q.17 A projectile of mass m is fired with velocity v pass a point A making an angle 45 with the horizontal.
Neglecting air resistance, the magnitude of change in momentum between the starting point A and the arriving
point B is
(a)
2 mv
(b)
2 mv
(c)
(1 - 2) m v
(d)
(mv)1/2
Q.18 A particle is thrown with a speed u at an angle  with the horizontal. When the particle makes an angle  with
the horizontal, its speed changes to v, which is equal to
(a)
u cos 
(b)
u cos  cos  (c)
u cos  sec  (d)
u sec  cos 
Q.19 A cannon ball has the same range R on a horizontal plane for two angles of projection. If h 1 and h2 are the
greatest heights in the two paths for which this possible, then
(a)
R = (h1h2)1/4
(b)
R = h1h2
(c)
R = 4 h1h2
(d)
R = h1h2
Q.20 Two balls are projected making angles of 30 and 45 respectively with the horizontal. If both have same
velocity at th4e highest point of their path, then the ratio of their horizontal range is
(a)
1:3
(b)
3: 1
(c)
3: 2
(d)
1: 3
Q.21 A particle is projected at an elevation tan-1 (5/3) from a point O. The ratio of the range on the horizontal plane
through O to the greatest height ascended above O is
(a)
2
(b)
2.4
(c)
0.4
(d)
1.5
Q.22 After one second the velocity of a projectile makes an angle of 45 with the horizontal. After another one second
it is traveling horizontally. The magnitude of its initial velocity and angle of projection are (g = 10 m/sec2)
(a)
14.62 ms-1, tan-1 (2)
(b)
22.36 ms-1, tan-1 (2)
(c)
14.62 ms-1, 60
(d)
22.36 ms-1, 60
Q.23 A particle is projected from the ground with an initial speed of u at an angle  with horizontal. The average
velocity of the particle between its point of projection and highest point of trajectory is
(a)
u cos 
(b)
u/2 1 + cos2 
2
(c)
u/2 1 + 2cos 
(d)
u/2 1 + 3 cos2 
Q.24 The maximum height attained by a projectile is increased by 5%. Keeping the angle of projection constant, what
is percentage increase in the horizontal range?
(a)
5%
(b)
10%
(c)
15%
(d)
20%
Q.25 The maximum height attained by a projectile is increased by 10%. Keeping the angle of projection constant,
what is percentage increase in the time of flight?
(a)
5%
(b)
10%
(c)
20%
(d)
40%
Q.26 The equation of motion of a projectile is :
y = 12x – 3/4 x2
The horizontal component of velocity is 3ms-1. Given that g = 10 ms-2, what is the range of the projectile?
(a)
12.4m
(b)
21.6m
(c)
30.6 m
(d)
36.0 m
Q.27 A body is projected is up a smooth inclined plane with velocity V from the point A as shown in the figure. The
angle of inclination is 45 and the top is connected to a well of diameter 40 m. If the body just manages to cross
the well, what is the value of V? Length of inclined plane is 202 m.
(a)
40 ms-1
(b)
402 ms-1
(c)
20 ms-1
(d)
202 ms-1
Q.28 Galileo writes that for angles of projection of a projectile at angles (45 + ) and (45 - ), the horizontal ranges
described by the projectile are in the ratio of :
(a)
2:1
(b)
1:2
(c)
1:1
(d)
2:3
Q.29 A projectile is fired from level ground at an angle  above the horizontal. The elevation angle  of the highest
point as seen from the launch point is related to  by the relation :
(a)
tan  =1/4 tan 
(b)
tan  = tan 
(c)
tan  = 1/2 tan 
(d)
tan  = 2 tan 
Q.30 Which of the following is the essential characteristic of a projectile?
(a)
Initial velocity inclined to the horizontal
(b)
Zero velocity at the highest point
(b)
Constant acceleration perpendicular to the velocity
(c)
None of the above
ANSWERSHEET
Projectile Motion
10
1.
(d)
2.
(b)
3.
(d)
4.
(b)
5.
(a)
6.
(c)
7.
(a)
8.
(a), (b)
9.
(c)
10.
(c)
11.
(c)
12.
(a)
13.
(c)
14.
(a)
15.
(d)
16.
(b), (d)
17.
(a)
18.
(c)
19.
(c)
20
(d)
21.
(b)
22.
(b)
23.
(d)
24.
(a)
25.
(a)
26.
(b)
27.
(d)
28.
(c)
29.
(c)
30.
(d)
11
Law of Motion
Q.1
Q.2
Q.3
Q.4
Q.5
Q.6
Q.7
Q.8
Q.9
Q.10
Q.11
A man is pulling on a rope attached to a block on a smooth horizontal surface. The tension in the rope will be
the same at all of its points–
(a)
if and only if the rope is not accelerating
(b)
if and only if the rope is massless
(c)
if and only if the rope is massless and not accelerating
(d)
if either the rope is massless or not accelerating
A block of mass M is pushed along a horizontal surface by a rope of mass m. Force F is applied at one end of the
rope. The force which the rope exerts on the block is
(a)
FM / (M – m)
(b)
FM / (M + m)
(c)
Fm / (M + m) (d)
Fm (M - m)
A 45kg load is being pulled vertically by a rope whose breaking strength is 495N. With what maximum
acceleration the load can be pulled up? (g = 10m/s2)
(a)
11m/s2
(b)
10m/s2
(c)
1m/s2
(d)
21m/s2
With what minimum acceleration can a fireman slide down a rope where breaking strength is two – thirds of its
weight?
(a)
2/3g
(b)
g
(c)
1/3g
(d)
zero
A body of mass 0.1kg is suspended from a massless string. The point of suspension moves (I) up (ii) down with
an acceleration of 5m/s2. If the tension in newtons in the string in the two cases are T1 and T2 respectively, then
(a)
T1 = T2
(b)
T2 - T1 = 1
(c)
T1 - T2 = 1
(d)
T1 - T2 = 2
If the tension in the cable of 100kg elevator is 1000kg weight, the elevator
(a)
is accelerating upwards
(b)
is accelerating downwards
(c)
may be at rest or accelerating
(d)
may be at rest or in uniform motion.
Two masses of 10kg and 20kg respectively are connected by a massless spring kept on a horizontal smooth
table. A force of 200N acts on the 20kg mass. At a given instant if the 10kg mass has an acceleration of 12m/s 2.
What is the acceleration of 20kg mass?
(a)
zero
(b)
10m/s2
(c)
4m/s2
(d)
12m/s2
A 2kg mass pulls horizontally on a 3kg mass by means of a lightly stretched spring. If at one instant the 3kg
mass has an acceleration towards 2kg mass 0f 1.8m/s2, the acceleration of 2kg mass is
(a)
1.2 m/s2
(b)
3.6 m/s2
(c)
2.7 m/s2
(d)
zero
An elevator starts from rest with a constant upwards acceleration. It moves 2.0m in the first 0.5s. A passenger in
the elevator is holding a 3kg package by a vertical spring. The tension in the spring is (Take g = 10m/s2)
(a)
36N
(b)
8N
(c)
30N
(d)
48N
Two masses 2kg and 1kg are connected by an inextensible string passing over a smooth fixed pulley. The
pressure in kg-wt on the axle of the pulley is
(a)
3kg.wt
(b)
1.5kg.wt
(c)
more than 3kg.wt
(d)
less than 3kg.wt
When a body is stationary :
(a)
there is no force acting on it
(b)
the forces acting on it are not in contact with it
(c)
the combination of forces acting on it balances each other
12
Q.12
Q.13
Q.14
Q.15
Q.16
Q.17
Q.18
Q.19
Q.20
Q.21
Q.22
Q.23
(d)
the body is in vacuum
When a body is in translatory equilibrium :
(a)
the body is definitely at rest
(b)
the body is definitely in the state of uniform motion
(c)
the body will be either at rest or in the state of uniform motion
(d)
none of the above
A body of mass 40 kg is hanging from the horizontal branch of a tree. The tension in his arms is minimum when
the angle between the arms is :
(a)
0
(b)
90
(c)
120
(d)
180
If a force of 250 N acts on a body, the momentum required is 125 m/s, what is the period for which force acts on
the body?
(a)
0.2 sec
(b)
0.5 sec
(c)
125  250 sec
(d)
0.25 sec
A man is rest in the middle of a pond on perfectly smooth ice. He can get himself to the shore by making use of
Newton’s :
(a)
first law
(b)
second law
(c)
third law
(d)
all the
news.
An elevator is moving vertically upwards with an acceleration of 6 m/s -2 ; the force exerted on the floor by the
man of mass 70 kg is :
(a)
420 N
(b)
70(6 + 9.8)N
(c)
70 (-6 + 9.8)N
(d)
70  9.8 N.
A balloon has 8 gram of air. A small hole is pierced into it. The air escapes at a uniform rate of 7 cms -1. If the
balloon shrinks in 5.6 seconds then the average force acting on the balloon is :
(a)
10-4 N
(b)
10-2 dyne
(c)
56 dyne
(d)
10-6 dyne.
A toy of mass 1 kg is placed on a spring balance. Suddenly, the toy jumps upwards. When it happens, the
reading of the spring balance changes from 1 kg to 1.10 kg. What will be the maximum value of the upward
acceleration of the toy? Take g = 10 ms-2.
(a)
1 ms-2
(b)
0.1 ms-2
(c)
0.01 ms-2
(d)
0.001 ms-2.
A rocket of mass 120 kg is fired in the gravity free space. It ejects gases with velocity 600 ms -1 at the rate of 1
kg/s. What will be the initial acceleration of the rocket?
(a)
1 ms-2
(b)
5 ms-2
(c)
10 ms-2
(d)
15 ms-2.
A machine gun is mounted on a 2000 kg vehicle on a horizontal smooth road (friction negligible). The gun fires
10 bullets per sec with a velocity of 500 m/s. If the mass of each bullet be 10g, what is the acceleration produced
in the vehicle?
(a)
25 cm/s2
(b)
25 m/s2
(c)
50 cm/s2
(d)
50 m/s2.
A body of mass M is acted upon by a force F and the acceleration produced is a. If there forces each equal to F
and inclined to each other at 120 act on the same body, the acceleration produced will be :
(a)
2a
(b)
a/3
(c)
3a
(d)
zero.
A packet of weight W is dropped with the help of a parachute and on striking the ground comes to rest with a
retardation equal to twice the acceleration due to gravity. What is the force exerted on the ground?
(a)
W
(b)
2W
(c)
3W
(d)
4W.
A dish of mass 10 g is kept floating horizontally in the air by firing bullets each of mass 5g with the same
velocity. If 10 bullets are fired per second and the bullets rebound with the same velocity, then the velocity of
each bullet is :
13
(a)
(c)
Q.24
Q.25
Q.26
Q.27
Q.28
Q.29
Q.30
196 cm/sec
49 cm/sec
(b)
(d)
98 cm/sec
none of these.
An object is resting at the bottom of two strings which are inclined at angle of 120 with each other. Each string
can withstand a tension of 20 N. The maximum weight of the object that can be sustained without breaking the
string is :
(a)
10 N
(b)
20 N
(c)
202 N
(d)
40 N.
A wagon weighing 1000 kg is moving with velocity 50 km/h on smooth horizontal rails. A mass of 250 kg is
dropped into it. The velocity with which it moves now is :
(a)
12.5 km/h
(b)
20 km/h
(c)
40 km/h
(d)
50 km/h.
A gun of mass 10 kg fires 4 bullets per seconds. The mass of each bullet is 20 kg and the velocity of the bullet
when it leaves the gun is 300 ms-1. The force required to hold the gun when firing is :
(a)
6N
(b)
8N
(c)
24 N
(d)
40 N.
Bullets of 0.03 kg mass each hit a plate at the rat of 200 bullets per second, with a velocity of 50 m/sec and
reflect back with a velocity of 30 ms-1. The average force acting on the plane in Newton is :
(a)
120
(b)
180
(c)
300
(d)
480.
A ball of mass 0.5 kg moving with a velocity of 2ms -1 strikes a wall normally and bounces back with the same
speed. If the time of contact between the ball and the wall is 10-3 sec, the average force exerted by the wall on
the ball is :
(a)
1125 N
(b)
1000 N
(c)
500 N
(d)
2000 N.
A 4000 kg rocket is set for firing. If the exhaust speed is 1000 ms-1, the mass to be ejected per second to just
overcome gravitational pull (g = 10 ms-2) is :
(a)
20 kg
(b)
10 kg
(c)
5 kg
(d)
40 kg.
A truck, weighing 8000 kg, is moving along a track with negligible friction at 1.8 ms -1 with the engine turn off
when it begins to rain hard. The raindrops fall vertically with respect to the ground. The speed of the truck,
when it has collected 1000 kg of rain water, is :
(a)
1.6 ms-1
(b)
10 ms-1
(c)
3ms-1
(d)
9 ms-1.
Law of Motion
1.
(d)
2.
(b)
3.
(c)
4.
(c)
5.
(c)
6.
(d)
7.
(c)
8.
(c)
9.
17.
25.
(b)
(a)
(c)
10.
18.
26.
(d)
(a)
(c)
11.
19.
27.
(c)
(b)
(d)
12.
20.
28.
(c)
(a)
(d)
13.
21.
29.
(a)
(d)
(d)
14.
22.
30.
(b)
(c)
(a)
15.
23.
(c)
(b)
16.
24.
(b)
(b)
FRICTION
Q.1
Q.2
Q.3
Q.4
Q.5
A uniform chain of length l lies on a rough table with coefficient of friction . What maximum portion of its
length can overhang from the edge of the table without sliding down?
(a)
l/
(b)
l / +1
(c)
l / +1l
(d)
l /  -1 l
A block of mass 2kg rests on a rough inclined plane making an angle of 30 with the horizontal. The coefficient
of static friction between the block and the plane is 0.7. The frictional force on the block is
(a)
9.8N
(b)
(0.7) (9.8) (3)N
(c)
(9.8)3N
(d)
(0.7) (9.8) N
A given body takes n times as much time to slide down a 45 rough incline as it takes to slide down a perfectly
smooth 45incline. The coefficient of kinetic friction between the body and the incline is given by
(a)
[1- 1/n2]
(b)
1/ [1- n2]
(c)
[1- 1/n2] (d) [1/1-n2]
A block of mass 0.1 kg is held against a wall by applying a horizontal force of 5N on the block. If the coefficient
of friction between the block and the wall is 0.5, the magnitude of the frictional force acting on the block is
(a)
2.5N
(b)
0.98N
(c)
4.9N
(d)
0.49N
Of the following forces of friction, the one which is self-adjusting is :
14
Q.6
Q.7
Q.8
Q.9
Q.10
Q.11
Q.12
Q.13
Q.14
Q.15
Q.16
Q.17
Q.18
Q.19
(a)
rolling friction
(b)
sliding friction
(c)
static friction
(d)
rolling friction
The maximum static frictional force depends on :
(a)
area of surfaces in contact
(b)
normal reaction
(c)
direction of applied force
(d)
none of the above
The static friction is:
(a)
equal to the dynamic frication
(b)
always less than the dynamic friction
(c)
always greater than the dynamics friction
(d)
sometimes greater and sometimes equal to dynamic friction
If the normal reactional force is doubled, the coefficient of friction is :
(a)
doubled
(b)
halved
(c)
not changed
(d)
tripled
Which of the following statements is false?
(a)
Force of friction is independent of macroscopic area of the surface in contact
(b)
Force of friction depends on the nature of materials of the surfaces in contact (i.e., force of
adhesion)
(c)
Force of friction does not depends on the rela5tive velocity between the surfaces
(d)
Force of friction is independent of roughness or smoothness of the surfaces in contact
Friction :
(a)
does not affect the efficiency of a machine
(b)
increases the efficiency of a machine
(c)
decreases the efficiency of a machine
(d)
noting can be said about the effect of friction on efficiency of a machine
Friction :
(a)
(b)
(c)
(d)
always opposes the motion of a moving body
may cause the motion of the body
is a conservative force
none of the above
The frictional force between two surfaces is independent of :
(a)
nature of surface`
(b)
size of the body
(c)
area of contact
(d)
mass of the body
A block mass 2 kg is placed on the floor. The coefficient of static friction is 0.4. If a force of 2.8 N is applied on
the block parallel to the floor, the force of friction between the block and floor (taking g = 10 ms-2) is :
(a)
2.8 N
(b)
8N
(c)
2N
(d)
zero
A block has been placed on an inclined plane. The slope angle  of the plane is such that the block slides down
the plane at a constant speed. The coefficient of kinetic friction is equal to :
(a)
sin 
(b)
cos 
(c)
g
(d)
tan 
If k is the coefficient of kinetic friction, f the coefficient of rolling friction and s the coefficient of static
friction then generally :
(a)
s > k > r
(b)
s < k < r
(c)
s < k > r
(d)
s > r > k
A block of 10 kg is pulled by a constant speed on a rough horizontal surface by a force of 19.6 N. The
coefficient of friction is :
(a)
0.1
(b)
0.2
(c)
0.3
(d)
0.4
A man walks over a rough surface, the angle between the force of friction and the instantaneous velocity of the
person is
(a)

(b)
/2
(c)
2
(d)
zero
A lift is moving upwards with a uniform velocity v in which a block of mass m is lying. The frictional force
offered by the block, when coefficient of friction is , will be :
(a)
zero
(b)
mg
(c)
mg
(d)
2mg
A body starts sliding down at an angle  to the horizontal. Then coefficient of friction is equal to :
(a)
sin 
(b)
cos 
(c)
tan 
(d)
cot 
15
Q.20
Q.21
Q.22
When a bicycle is in motion but not pedaled, the force of friction exerted by the ground on the two wheels is
such that it acts :
(a)
in the backward direction on the front wheel and in the forward direction on the rear wheel
(b)
in the forward direction on the front wheel and in the backward direction on the rear wheel
(c)
in the forward direction on both the wheels
(d)
in the backward direction on both the wheels
Pulling force making an angle  to the horizontal is applied on a block of weight W place on a horizontal table.
If the angel of friction is , the magnitude of force required to move the body is equal to :
(a)
W cos  / cos ( -)
(b)
W sin  / cos ( -)
(c)
W tan  / sin ( -)
(d)
W sin  / tan ( -)
In the case of pulling a cart, the force that causes the horse to move forward is that force :
(a)
the horse exerts on the ground
(b)
the horse exerts on the cart
(c)
the ground exerts on the horse
(d)
the cart exerts on the horse
ANSWER
Friction
1.
9.
17.
(c)
(d)
(d)
2.
10.
18.
(a)
(c)
(a)
3.
11.
19.
(a)
(b)
(b)
4.
12.
20.
(b)
(c)
(c)
5.
13.
21.
(c)
(a)
(c)
6.
14.
22.
(b)
(d)
(a)
7.
15.
(c)
(a)
8.
16.
(c)
(b)
CIRCULAR MOTION
Q.1
Q.2
Q.3
Q.4
Q.5
Q.6
Q.7
Q.8
A car travelling at 20m/s on a circular road of radius 100m. It is increasing in speed at the rate of 3m/s 2. Its
acceleration is
(a)
3m/s2
(b)
4m/s2
(c)
5m/s2
(d)
3m/s2
A particle P is moving in a circle of radius R with a uniform speed. The centre of the circle is C and AB is a
diameter. The angular velocity of P about A and C are in the ratio of
(a)
1:1
(b)
1:2
(c)
2:1
(d)
4:1
The linear velocity and the angular velocity  are related to each other by the following relation, where r is the
radius vector of the particle with respect to the center
(a)
=r
(b)
=r
(c)
=r
(d)
 = r
A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The
motion of the particle takes place in a plane. It follows that
(a)
its velocity is constant
(b)
its acceleration is constant
(c)
its kinetic energy is constant
(d)
it moves in a circular path
Two cars of masses m1 and m2a are moving along the circular path of radii r1 and r2. They take one round
in the same time. The ratio of their angular speeds 1/2 is
(a)
m1/ m2
(b)
r1 / r2
(c)
1:1
(d)
m1r1/m2r2
If a flyover is concave of radius R instead of being convex, the thrust at the lowest position on a car of mass m
travelling with speed  will be
(a)
mg + m2/R
(b)
mg - m2/R
(c)
mg
(d)
mg + mR
The string of a pendulum of length l is displaced through 90 from the vertical and released. Then the minimum
strength of the string in order to withstand the tension as the pendulum passes through the mean position is
(a)
mg
(b)
3 mg
(c)
5 mg
(d)
6 mg
A simple pendulum of length l having a bob of mass m is oscillating in a plane about a vertical line between
angular limits - and +. For an angular displacement (), the tension in the string and the velocity of the
bob are T and  respectively, the following relation holds good under the above conditions.
(a)
T = mg cos
(b)
T cos  = mg
2
(c)
T - mg cos = mv /l
(d)
+ mg cos  = mv2/l
16
Q.9
Q.10
Q.11
Q.12
Q.13
Q.14
Q.15
Q.16
Q.17
Q.18
Q.19
Q.20
A 1 kg stone at the end of 1m long string is whirled in a vertical circle such that a constant speed of 4m/s is
maintained. The tension in the string is 6N when the stone is
(a)
at the bottom of the circle
(b)
at the top of the circle
(c)
half way down
(d)
none of these above.
A can filled with water is revolved in a vertical circle of radius 4m, the water does not fall down. The time
period for a revolution will be about
(a)
2s
(b)
10s
(c)
8s
(d)
4s
A bucket filled with water is whirled in a vertical circle with a string attached to it. The water does not fall even
when the bucket is in inverted position at the top of its path. It is therefore, concluded that
(a)
mg is equal to mv2/R
(b)
mg is greater than mv2/R
2
(c)
mg is not greater than mv /R
(d)
mg is not less than mv2/R
A smooth hemispherical bowl 0.30 m in diameter, rotates with a constant angular velocity  about its vertical
axis of symmetry such that a particle of mass 0.5kg remain at rest, relative to the bowl at a height 0.10 m above
the base. The magnitude of  in radians per seconds is
(a)
8
(b)
14
(c)
4.5
(d)
3
A sphere of mass 100 gm is attached to inextensible string of length 1.3m whose upper end is fixed in the
ceiling. The sphere is made to describe a horizontal circle of radius 50cm. The time period of one revolution is
(a)
5.0s
(b)
4.5s
(c)
3.2s
(d)
2.4s
A coin is placed on a rotating turn table just slips if it is placed at a distance of 4cm from the centre. If the
angular velocity of the turn - table is doubled, it will just slip at a distance of
(a)
1cm
(b)
2cm
(c)
4cm
(d)
8cm
A uniform ring of radius r and mass per unit length  is spun about its axis with an angular velocity . The
increase in tension in the ring is
(a)
 r2 2
(b)
 r 2
(c)
 r2 
(d)
 r2 3
The maximum tension which an inextensible ring of mass 0.1kg/m can bear is 10N. The maximum velocity in
m/s with which it can be rotated is
(a)
10
(b)
10
(c)
20
(d)
15
A car is going with a constant speed on an over bridge of circular shape. As the car is ascending on the bridge,
the normal force on the car due to the bridge
(a)
increase
(b)
decrease
(c)
remains same (d)
fluctuates
A particle of mass m rotates in X-Y plane in a circle of radius a with a uniform angular speed . It is viewed
from a frame rotating about Z-axis with a uniform angular speed 0. The centrifugal force on the particle is
(a)
m 2a
(b)
m 02a
(c)
m (+0 / 2)2 a
(d)
m 0a
A person applies a constant force F on a particle of mass m and finds that the particle moves in a circle of radius
r with a uniform speed  as seen from the inertial frame of reference.
(a)
This is not possible
(b)
There are other forces on particle
2
(c)
The resultant with the other forces is mv /r towards the centre
(d)
The resultant with other forces varies in magnitude as well as in direction
A particle is moving in a vertical circle of radius a. Its speed vat its lowest point is sufficiently great for the
particle to describe complete circles. When the string is horizontal the speed of the particle is
(a)
(c)
Q.21
2ga
v2 - 2ga
(b)
(d)
v2 + 2ga
v2 + ga
A mass of 2kg is whirled in a horizontal circle by means of a string at an initial speed of 5rpm. Keeping the
radius constant, the tension in the string is doubled. The new speed is nearly
(a)
14rpm
(b)
10rpm
(c)
20rpm
(d)
7rpm
17
Q.22
Q.23
Q.24
A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ac is
varying with time t as ac = k2 rt2 where k is constant. The power delivered to the particle by the forces acting on
it is
(a)
2 k2r2t
(b)
mk2r2t
(c)
(mk4r2t5)/3
(d)
zero
A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The
tube is then rotated in a horizontal plane about one of its end with a uniform angular velocity . The forces
acting exerted by the liquid at the other end is
(a)
M 2 L/2
(b)
M2L
(c)
M2 L/4
(d)
M2 L3/2
A hollow cone is fixed with its axis vertical and vertex down. A particle is describing circular motion in contact
with the inside surface of the cone in a horizontal plane at a height h above the vertex. If the inside surface is
frictionless, then the velocity of particle is
(a)
gh
(b)
2gh
(c)
gh/2
(d)
3gh/2
ANSWER
1.
(c)
2.
(b)
3.
(c)
4.
(c), (d)
5.
(c)
6.
(a)
7.
(b)
8.
(c)
9.
(b)
10.
(d)
11.
(c)
12.
(b)
13.
(d)
14.
(a)
15.
(a)
16.
(a)
17.
(a)
18.
(b)
19.
(b), (c)
20.
(c)
21.
(d)
22.
(b)
23.
(a)
24.
(a)
18
WORK, POWER, ENERGY
Q.1
Q.2
Q.3
Q.4
Q.5
Q.6
Q.7
Q.8
Q.9
Q.10
Q.11
A 2kg body falls vertically and strikes and strikes the floor with a speed of 10m/s. It rebounds with a speed of
4m/s. The magnitude of impulse on the ball during the impact is
(a)
8Ns
(b)
12Ns
(c)
20Ns
(d)
28Ns
Two masses of 1kg and 4kg are moving with equal kinetic energies. The ratio of the magnitudes of their linear
momentum is
(a)
4:1
(b)
1 : 2
(c)
1:2
(d)
1 : 16
A projectile of mass m is fired with a speed  at an angle of 45 with the horizontal from a point P and reaches
Q in the same horizontal plane. Neglecting air resistance, the magnitude of change in momentum between its
leaving P and arriving at Q is
(a)
zero
(b)
½ mv
(c)
mv2
(d)
2mv
A radioactive nucleus initially at rest decays by emitting an electron and neutron at right angles to each other.
The momentum of the electron is 3.2  10-23 kg ms-1 and that of neutron is 6.4 10-23 kg ms-1. The direction of
recoiling nucleus with that of electron motion is
(a)
tan-1(0.5)
(b)
tan-2(2)
(c)
-tan-1(2)
(d)
+tan-1(2)
A body of mass 1 kg initially at rest, explodes and breaks into three fragment of masses in the ratio of 1:1:3. The
two pieces of equal mass fly off perpendicular to each other, with a speed of 30m/s each. What is the velocity of
the heavier fragment?
(a)
10m/s
(b)
20m/s
(c)
102m/s
(d)
302m/s
Two trains X and Y are running parallel to each other in the same direction on frictionless rails. The train X is
faster than the train B. Now, if as a consequence of exchange of packets of equal masses between them, the
acceleration of train X is a1 and that of train Y is a2, then
(a)
a1 is-ive, a2is+ive
(b)
a1 is+ive, a2is-ive
(c)
a1=0, a2 is +ive
(d)
a2=0, a1 is +ive
A ball hits the floor and rebounds after inelastic collision. In this case
(a)
the momentum of the ball just after the collision is the same as that just before the collision.
(b)
the mechanical energy of the ball remains the same in the collision.
(c)
the total momentum of the ball and the earth is conserved
(d)
the total energy of the ball and the earth is conserved.
The bob of a simple pendulum of mass m and length l is dropped from is horizontal position. As a consequences
it strikes elastically a block of the same mass placed on the horizontal frictionless table. The kinetic energy of
the block after collision will be
(a)
2mgl
(b)
mgl
(c)
½ mgl
(d)
0
A ball is dropped from a height h on the ground. If the coefficient of restitution is e, the height to which the ball
goes up after it rebounds for nth time is
(a)
he2n
(b)
hen
(c)
h/en
(d)
h/e2n
A ball hits a fixed surface with a velocity u at an angle  with the normal to the surface at the point of impact
and rebounds from it an angle  with the normal to the surface. If the coefficient of restitution for the impact is
e, then
(a)
=
(b)

(c)
tan=e tan 
(d)
tan=1/e tan 
The head of a hammer weight 1.5kg. It falls from a height of 0.8 m and strikes a nail and drives it into a wooden
block. The duration of impact is 0.005 s and g=10m/s2. The average impact force exerted by the hammer is
(a)
Q.12
(b)
1500N
(c)
1200N
(d)
750N
A hammer with a 1kg head is used to derive nails horizontally into a wooden vertical wall. A force of 900 N is
required to penetrate the wood. Each blow should force the nail 5mm into the wall. The velocity of the hammers
head when it strikes the nail is
(a)
Q.13
3000N
9m/s
(b)
6m/s
(c)
3m/s
(d)
1m/s
A body of mass 0.5 kg moving at a speed of 4m/s colludes with another body of mass 1.0kg. After the collision
the two bodies stick together and remain motionless. The velocity of 1.0kg mass before impact is
19
(a)
Q.14
Q.20
Q.22
(b)
5J
(c)
1.5J
(b)
2J
(c)
48J
(b)
32J
(c)
100%
(b)
95%
(c)
zero
(b)
½a
(c)
depends on masses of the balls
(b)
depends on directions of motion of balls
(c)
(d)
depends both on masses and direction of motion
is equal to Ig.
6J
(d)
16J
4J
(d)
5J
24J
(d)
288J
5%
(d)
50%
a
(d)
2a
Two particles A and B initially at rest, move towards each other under a mutual force of attraction. At the instant
when the speed of A is v and the speed of B is 2v, the speed of the center of mass of the system is
zero
(b)
v
(c)
1.5v
(d)
2v
A bomb travelling in a parabolic path under the effect of gravity explodes in mid air. The center of mass of the
fragments will continue to move
(a)
along a hyperbolic path
(b)
vertically upwards and then vertically downwards
(c)
horizontally in the forward direction
(d)
along the original parabolic path.
Masses of 4 kg and 12kg are approaching each other on a frictionless surface with speeds 6m/s eastward and
10m/s westward respectively. The velocity of the center of mass is
4m/s east
(b)
6m/s west
(c)
8 m/s east
(d)
0
A boat of mass 45kg is floating in still water. A dog of mass 15kg walks from the stern to the bow. The length of
the boat is 3m. What distance does the boat move?
(a)
Q.24
4J
(a)
(a)
Q.23
–4m/s
Two balls of unequal masses are thrown simultaneously in air. The acceleration of the center of mass of the two
balls while in air
(a)
Q.21
(d)
Consider two particles of equal masses. One of the particles is at rest while the other is moving with a constant
acceleration a. The center of mass of the system of the two particles has an acceleration
(a)
Q.19
–2m/s
A 50g bullet moving with velocity 10m/s strikes a block of mass 950g at rest and gets embedded in it. The loss
of kinetic energy will be
(a)
Q.18
(c)
A bomb of 12kg explodes into two pieces of masses 4kg and 8kg. The velocity of 8kg mass is 6m/s. The kinetic
energy of the other mass is
(a)
Q.17
zero
A bomb of mass 3kg which is at rest explodes into three fragment of equal masses. Two of the fragment are
found to move with a speed of 1m/s each in mutually perpendicular directions. The total energy released during
explosion is
(a)
Q.16
(b)
Two bodies each of mass 1kg move towards each other in mutually perpendicular directions with velocities
4m/s and 2m/s. If the two bodies sticks together after collision, the heat liberated will be
(a)
Q.15
2m/s
1.5m
(b)
1.0m
(c)
Internal forces can change
(a)
(b)
linear momentum but not kinetic energy
kinetic energy but not linear momentum
(c)
both linear momentum and kinetic energy
(d)
neither linear momentum nor kinetic energy
20
0.75m
(d)
0.25m
Q.25
A body is moved along a straight line by a machine delivering a constant power. The distance travelled by the
body in time t is proportional to
(a)
Q.26
Q.28
(C)
t3/2
(d)
t2
mgl
(b)
1/3 mgl
(c)
1/9 mgl
(d)
1/18 mgl
(a)
5
(b)
10
(c)
20
(d)
120
If g is the acceleration due to gravity on the earth’s surface, the gain in potential energy of an object of mass m
raised from the surface of the earth to a height equal to radius R of the earth is
mg R/2
(b)
2 mg R
(c)
mg R
(d)
¼ mg R
When the mass of 20g is hanged to one end of a light spring of length 10cm, the spring is stretched by 2cm. The
mass is pulled down until the total length of the spring is 14cm. The elastic energy in J, stored in the spring is
(a)
Q.30
t3/4
A lift pump works normally at 200V, 10A. It pumps water to an average height of 15m to fill a tank of volume
3m2m1m. If the efficiency of the pump is 75%, the time in minute required to fill the tank is nearly
(a)
Q.29
(b)
A uniform chain of length l and mass m is lying on a smooth table and one third of its length is hanging
vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the
hanging part on the table is
(a)
Q.27
t1/2
8  10-2
(b)
4  10-2
(c)
2  10-3
(d)
8  10-3
A block of mass 1kg is permanently attached with a spring of spring constant k=100N/m. The spring is
compressed 0.20m and placed on a horizontal smooth surface. When the block is released, it moves to a point 04m beyond the point when the spring is at its natural length. The work done by the spring in changing from
compressed state to the stretched state is
(a)
10J
(b)
–6J
(c)
–8J
(d)
18J
ANSWER SHEET
1.
(d)
2.
(c)
3.
(c)
4.
(d)
5.
(c)
6.
(a)
7.
(c)
8.
(b)
9.
(a)
10.
(d)
11.
(c)
12.
(c)
13.
(c)
14.
(b)
15.
(b)
16.
(d)
17.
(b)
18.
(b)
19
(d)
20.
(a)
21.
(d)
22.
(b)
23.
(c)
24.
(b)
25.
(c)
26.
(d)
27.
(b)
28.
(a)
29.
(d)
30.
(b)
21
Gravitation
Q.1
Q.2
Q.3
Q.4
Q.5
Q.6
Q.7
Q.8
Q.9
Q.10
Q.11
Q.12
Two particles of mass m and M are initially at rest and infinitely separated from each other. Due to gravitational
attraction they approach each other. Their relative velocity of approach at a separation r between them is
(a)
[Gr /M + m]1/2
(b)
[2G(M + m)/r]1/2
(c)
2G (M + m)1/2
(d)
2Gr(M + m)
Four particles, each of mass 1kg are at the corners of a square of side 1m. The work which must be done to
remove on of the particle of infinity is
(a)
22G
(b)
(22+1)/2 G
(c)
(22+1) G
(d)
3G
Three particles of mass m each are placed at the three corners of an equilateral triangle of side a. The work
which should be done to increase the sides of the triangle to 2a is
(a)
3Gm2 / a
(b)
3Gm2 / 2a
2
(c)
Gm / 2a
(d)
3Gm / 2a
The gravitational force of attraction on a unit mass particle placed at a distance of r from the centre and on the
axis of a uniform ring of mass M and radius R is
(a)
GM/r2
(b)
GM/R2
2
2 3/2
(c)
GM r/ (r +R )
(d)
GM/ (r2+R2)
A particle of mass 1kg is placed at a distance of 4m from the centre and on the axis of a uniform ring of mass
5kg and radius 3m. The work done to increase the distance of the particle from 4m to 33m in joules is
(a)
G/3
(b)
G/4
(c)
G/5
(d)
G/6
Inside a uniform spherical shell
(a)
the gravitational potential is zero
(b)
the gravitational field is zero
(c)
the gravitational potential is same everywhere
(d)
the gravitational field is proportional to distance from the centre.
If the radius of the earth is reduced by 1% keeping its mass unchanged, the change in the acceleration due to
gravity is
(a)
2% increase
(b)
1% increase
(c)
2% decrease
(d)
1% decrease
9
A star suddenly shrinks and its density becomes 10 times its original value. The value of acceleration due to
gravity on its surface will increase by a factor of
(a)
10-9
(b)
10-6
(c)
106
(d)
109
2
The radius of the earth’s orbit is 6400km and g = 10m/s . In order that a body of 5kg weighs zero at equator, the
angular speed, in radians, of the earth should be
(a)
1/80
(b)
1/400
(c)
1/800
(d)
1/1600
The weight of a body as measured by a spring balance in a train at rest is W0, when the train begins to move with
velocity v around the equator from west to east and the earth is rotating with angular velocity , then the weight
shown by the spring balance is
(a)
W0
(b)
W0 (1+2v/g)
(c)
W0 (1-2v/g)
(d)
W0 (1+v2/g)
Two identical trains are moving on rails along the equator on the earth in opposite directions with the same
speed. The train A is moving towards east and the train B towards west. The pressure exerted on the rails will be
(a)
same due to both
(b)
zero due to both
(c)
more for train A
(d)
more for train B
If g be the acceleration due to gravity of the earth’s surface, the gain in the potential energy of an object of mass
m raised from the surface of the earth to a height equal to the radius R of the earth is
(a)
½ mgR
(b)
2mgR
(c)
mgR
(d)
¼ mgR
Aurora Classes
22
Gravitation
Q.13
Q.14
Q.15
Q.16
Q.17
Q.18
Q.19
Q.20
Q.21
Q.22
Q.23
Q.24
Q.25
Consider two planets with the same density but radii R1 and R2. The ratio of escape velocities v1/v2 from their
respective surfaces will be
(a)
(R2/R1)2
(b)
R2/R1
(c)
R1/ R2
(d)
(R1/ R2)2
A satellite is moving round the earth. In order to make it move to infinity, its velocity must be increased by
(a)
20%
(b)
41.4%
(c)
82.8%
(d)
100%
Two identical satellites revolving in the same orbit around the earth in the opposite directions make an inelastic
collision so that wreckage form one piece, then this piece of tangled material
(a)
will move in an orbit of half the original radius
(b)
will move in an orbit of one-fourth the radius
(c)
will escape to infinity
(d)
falls directly on the earth
A planet moves round the sun. At a point P it is closest to the sun at a distance d1and has a speed v1. At another
point Q, when it is farthest from the sun at a distance d2, its speed will be
(a)
d12v1/d22
(b)
d2v1/d1
(c)
d1v1/d2
(d)
d22v1/d12
Consider the following periodic motions(a)
A simple pendulum of infinite length will bob near the earth’s surface
(b)
A ball oscillating in a tunnel dug through the earth
(c)
A satellite revolving round the earth close to the earth’s surface
(d)
A satellite revolving round the earth at a height equal to the earth’s radius.
Which of the above periodic motions have the same period
(a)
1, 2, 3
(b)
2, 3, 4
(c)
3, 4, 1
(d)
4, 3, 2
The ratio of the kinetic energy required to give to the satellite to escape earth’s gravitational field to the kinetic
energy required to put the satellite in a circular orbit close to the earth’s surface is
(a)
1
(b)
2
(c)
½
(d)

A satellite of mass m is revolving round the earth at a height R above the surface of the earth, where R is the
radius of the earth. If g is the acceleration due to gravity at the surface of the earth, the kinetic energy of the
satellite is
(a)
¼ mgR
(b)
½ mgR
(c)
mgR
(d)
2mgR
The orbit velocity of an artificial satellite in a circular orbit just above the earth surface is v. The speed for
another orbiting at an altitude of half the earth’s radius is
(a)
3/2 v
(b)
[3/2]v
(c)
[2/3]v
(d)
2/3v
A satellite is orbiting the earth in a circular orbit of radius r. Its
(a)
kinetic energy varies as 1/r
(b)
linear momentum varies as 1/r
(c)
angular momentum varies as 1/r
(d)
frequency varies as 1/r3
Suppose the law of gravitational attraction suddenly changes and follows inverse cube law i.e., F  1/r3, then
(a)
Kepler’s law of areas still holds
(b)
Kepler’s law of period still holds
(c)
The laws of areas as well as the law of periods still hold
(d)
Neither the low of areas nor the law of periods remains valid.
The eccentricity of the earth’s orbit is 0.0167. The ratio of its maximum speed in its orbit to its minimum speed
is
(a)
2.507
(b)
1.033
(c)
8.324
(d)
1.000
A satellite moves round a planet in an elliptical orbit. The maximum and minimum distance of the planet from
the planet are r1 and r2 respectively. The time period of the satellite is proportional to
(a)
r13/2
(b)
r23/2
(c)
(r1+r2)3/2
(d)
(r1-r2)3/2
Two satellites A and B go around a planet P in circular orbits having radii 4R and R respectively. If the speed of
satellite A is 3 v, the speed of satellite B would be
(a)
12 v
(b)
6v
(c)
[4/3]v
(d)
(3/2)v
Aurora Classes
23
Gravitation
Q.26
If the distance between the earth and the sun were half at its present value, the number of days in a year would
have been
(a)
64.5
(b)
129
(c)
182.5
(d)
730
Q.27 When the body is moving up, the acceleration due to gravity will be:
(a)
Downward
(b)
Upward
(c)
Sideways
(d)
Nil
Q.28 At sea level the value of g is minimum at:
(a)
The equator
(b)
45 north latitude
(c)
45 south latitude
(d)
The pole
Q.29 As we go from the equator to the poles, the value of g :
(a)
Remains the same
(b)
Decrease
(c)
Increases
(d)
Decrease up to a latitude of 45 and then increases
Q.30 The value of g will be 1% of its value at the surface of earth at a height of (Re = 6400 km)
(a)
6400 km
(b)
57600 km
(c)
2560 km
(d)
64000 km
Answer Sheet
1.
6.
11.
16.
21.
26.
Aurora Classes
(b)
(b), (c)
(d)
(c)
(a), (b), (d)
(b)
2.
7.
12.
17.
22.
27.
(b)
(a)
(a)
(a)
(a)
(a)
3.
8.
13.
18.
23.
28.
24
(b)
(c)
(c)
(a)
(b)
(a)
4.
9.
14.
19.
24.
29.
(c)
(c)
(b)
(a)
(c)
(c)
5.
10.
15.
20.
25.
30.
(d)
(c)
(d)
(c)
(b)
(b)
Gravitation
Rotation Motion
Q.1
Two point masses (of mass m1 and m2) all joining by a massless string of length r. The
moment of inertia of the system about an axis passing through the centre of mass and
perpendicular to the string is
(a)
(m1 + m2) r2
(b)
m1 m2 /m1 + m2 r2
(c)
m1 / m2(m1 + m2) r2
(d)
m2 / m1 (m1+ m2) r2
Q.2
A closed tube partly filled with water lies in a horizontal plane. If the tube is rotated about a
perpendicular bisector, the moment of inertia of system
(a)
increase
(b)
decrease
(c)
remains constant
(d)
depends on sense of rotation
Q.3
A rod A B of mass m and length is rotating in a vertical plane about its fixed end A. A
particle of mass m is attached to its other end B. If the velocity of the particle when it is at
the lowest position, its velocity is
(a)
Q.4
Q.7
Q.9
(c)
4gl
(d)
3gl
½
(b)
1/3
(c)
¼
(d)
2/3
2/3
(b)
2/5
(c)
3/5
(d)
4/5
A particle moves with a constant velocity parallel to the axis. Its angular momentum with
respect to the origin
(a)
is zero
(b)
remains constant
(c)
goes on increasing
(d)
goes on decreasing
A small object of mass m is attached to a light string and made to rotate on a small
frictionless table in a circular path whose radius can be changed, by pulling the other end of
the string through the hole at the centre. If the initial and final values of the radius of the
orbit, speed and angular velocities of the object are r1, v1, 1 and r2, v2, 2 respectively, then
2/1 respectively
(a)
Q.8
5gl
A disc of mass M and radius R is rotating in a horizontal plane about an axis passing through
its centre and perpendicular to it which angular velocity . Another disc of half the radius
but double the mass is placed gently on the first coaxially. The new angular velocity of the
system will be
(a)
Q.6
(b)
A solid cylinder of mass m and radius r rolls down an inclined plane of height h. The friction
of the energy which is transformed into rotational kinetic energy is
(a)
Q.5
9gl
r1 / r2
(b)
(r1 / r2)2
(c)
( r2 / r1)2
(d)
r2 / r1
A thin circular ring of mass M and radius R rotates about its axis with a constant angular
velocity . Two equal masses, each of mass m are placed gently on to the ring. Now the
angular velocity of the ring is
(a)
M/M+m 
(b)
(M +2 m) / M 
(c)
(M -2 m) / (M +2 m) 
(d)
M / (M +2 m) 
A man standing on a horizontal turntable turning at a certain angular frequency, with his
arms folded has equal weights in his hands. When he stretches his arms horizontally, the
final kinetic energy of the system is
Rotation Motion
25
(a)
same as before
(b)
less than before because part of it is converted into potential energy
(c)
less than before because part of it is converted into heart
(d)
greater than before because part of potential energy is converted into kinetic
energy
Q.10 A loaded truck has to take a sharp turn to the left. The centre of gravity of the truck can be
altered by shifting a concentrated load. To avoid toppling, the load must be shifted
(a)
up and left
(b)
down and left
(c)
up and right
(d)
down and right
Q.11 A Ping-Pong ball is floating on the top of a vertical water jet. In the vertical direction it is in
the
(a)
stable equilibrium
(b)
unstable equilibrium
(c)
neutral equilibrium
(d)
equilibrium position
Q.12 A constant torque acting on a uniform circular wheel changes its angular momentum from
A0 to 4 A0 in 4 seconds. The magnitude of this torque is
(a)
3A0/4
(b)
4A0
(c)
A0
(d)
2A0
Q.13 For a system to be in equilibrium, the torques acting on it must balance. This is true only if
the torques are taken about
(a)
The centre of the system
(b)
the centre of mass of the system
(c)
any point on the system
(d)
any point on the system or outside
Q.14 A uniform horizontal metre scale of mass m is suspended but two vertical strings attached to
its two ends. A body of mass 2m is placed on the 75 cm mark. The tensions in the two
strings are in the ratio
(a)
1:2
(b)
1:3
(c)
2:3
(d)
3:4
Q.15 A flywheel rotate with a uniform angular velocity increases from 20 rad/s to 40 rad/s in
10seconds. How many rotations did it make in this period?
(a)
80
(b)
100
(c)
120
(d)
150
Q.16 When a ceiling fan is switched on, it makes 10 rotations in the first 3 seconds. How many
rotations will it make in the next 3 seconds? (Assume uniform angular acceleration)
(a)
10
(b)
20
(c)
30
(d)
40
Q.17 When a ceiling fan is switched off, its angular velocity falls to half while it makes 36
rotations. How many more rotations will it make before coming to rest? (Assume uniform
angular retardation)
(a)
36
(b)
24
(c)
18
(d)
12
Q.18 A flywheel rotates about an axis. Due to friction at the axis, it experiences an angular
retardation proportional to its angular velocity. If its angular velocity falls to half while it
makes n retardation. How many more rotations will it make before coming to rest ?
(a)
2n
Rotation Motion
(b)
n
(c)
n/2
(d)
n/3
26
Q.19 An external device, e.g., an electric motor, supplies constant power to a rotating system, e.g., a
flywheel, through a torque . The angular velocity of the system is . Both and are variable.
(a)
  
(b)
 1/
(c)
 
(d)
1/ 
Q.20 The radius of gyration of a thin disc of radius 4 cm about a diameter is
(a)
4 cm
(b)
22 cm
(c)
2 cm
(d)
2 cm
Q.21 The radius of gyration of a solid sphere of radius r about a certain axis is r. The distance of this
axis from the centre of the sphere is
(a)
r
(b)
0.5r
(c)
0.6r
(d)
0.4r
Q.22 If the radius of the earth becomes half of its present value, with its mass remaining the same, the
duration of one day will become
(a)
6h
(b)
12h
(c)
48 h
(d)
96 h
Q.23 A small ball strikes a stationary uniform rod, which is free to rotate, in gravity- free space. The
ball does not stick to the rod. The rod will rotate about
(a)
its centre of mass
(b)
the centre of mass of ‘rod plus ball’
(c)
the point of impact of the ball on the rod
(d)
the point about which the moment of inertia of the ‘rod plus ball’ is minimum
Q.24 A triangular frame in the form of an equilateral triangle of side a is formed by bending a uniform
thin bar of length 3a and mass M. The moment of inertia of the frame about an axis passing
through the center of mass an perpendicular to its plane is
(a)
½ Ma2
(b)
1/3 Ma2
(c)
1/6 Ma2
(d)
1/12 Ma2
Q.25 Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an
axis perpendicular to its plane and passing through a point on its rim will be :
(a)
5I
(b)
3I
(c)
6I
(d)
4I
Q.26 Let l be the moment of inertia of a uniform square plate about an axis AB that passes through its
centre and is parallel to two of its sides. CD is alone in the plane of the plate that passes through
the centre of the plate and makes an angle with AB. The moment of inertia of the plate about
the axis CD is then equal to
(a)
I
(b)
I sin2 

c)
I cos2 




d)
I cos2 (/2)
Q.27 Two circular discs are of the same thickness. The diameter of A is twice that of B. the moment of
inertia of A as compared to that of B is :
(a)
twice as large
(b)
four times as large 
c)
8 times as large



d)
16 times as large
Q.28 Moment of inertia comes into play :
(a)
In translatory motion
(b)
In rotatory motion
(a)
In vibratory motion
(b)
When the body is permanently at rest
Q.29 Moment of inertia plays the same role in rotatory motion as in translatory motion is played by :
(a)
Velocity
(b)
Acceleration (c)
Mass
(d)
Force
Q.30 The moment of inertia of a body does not depend on
(a)
The mass of the body
(b)
The angular velocity of the body
(c)
The axis of rotation of the body
(d)
The distribution of the mass in the body
Aurora Classes
Properties of Matter
27
Answer Sheet
1.
(b)
2.
(a)
3.
(a)
4.
(b)
5.
(a)
6.
(b)
7.
(b)
8.
(d)
9.
(b)
10.
(b)
11.
(a)
12.
(a)
13.
(d)
14.
(a)
15.
(d)
16.
(c)
17.
(d)
18.
(b)
19.
(b)
20.
(c)
21.
(c)
22.
(a)
23.
(a)
24
(c)
25.
(c)
26.
(a)
27.
(d)
28.
(b)
29.
(c)
30.
(b)
Aurora Classes
Properties of Matter
28
Properties of Matter
Q.1
An iron rod of length 1m and cross-sectional area 0.1 cm2 with Young’s modules 1011N/m2 is to be pulled
by applying force on its two ends so as to produce an elongation of 1mm. The force on each end is
(a)
Q.2
500N
(c)
2000N
(d)
100N
length 100cm, diameter 1mm
length 300cm, diameter 3mm
(b)
(d)
length 200cm, diameter 2mm
length 400cm, diameter 0.5mm
A wire can be broken by applying a load of 10kg wt. The force required to break the wire of the same
material but the twice the diameter and of the same length is
(a)
Q.4
(b)
Four wires of the same material are stretched by the same load. The dimensions are given below. Which
of them will elongate the most?
(a)
(c)
Q.3
1000N
5kg wt.
(b)
10kg wt.
(c)
20kg wt.
(d)
40kg wt.
A cable capable of supporting a load W is cut to half of its original length. The maximum load it can
support now is
(a)
W/2
(b)
W
(c)
2W
(d)
4W
Q.5
A spring of force constant k is cut into two equal pieces. The force constant of each piece is
Q.6
(a)
k/2
(b)
k
(c)
2k
If a gas is heated at constant pressure; its isothermal compressibility
Q.7
remains constant
(b)
increase linearly with temperature
(c)
decrease linearly with temperature
(d)
increase inversely with temperature
Two rods of different material having coefficients of liner expansion 1, 2 and Youngs modules Y1and
Y2 respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the
same increase in temperature. There is no bending of rods, if 1:2=2:3, the thermal stresses developed in
the two rods are equal provided Y1:Y2 is equal to
(b)
1:1
(c)
3:2
(d)
4:9
1/3 (R2-r2) hg
(b)
r2 hg
(c)
R2 hg
(d)
[r+R/2]2hg
An open vessel containing some liquid is given a constant acceleration a in the horizontal direction. The
free surface of the liquid gets sloped with the horizontal at an angle  given by
(a)
Q.10
2:3
A uniformly tapering vessel of height h whose lower and upper radii are r and R is completely filled with
a liquid of density . The force that acts on the base of the vessels due to the liquid is
(a)
Q.9
4k
(a)
(a)
Q.8
(d)
tan  =a/g
(b)
tan  =g/a
(c)
sin  =a/g
(d)
cos  =g/a
A U-tube stands vertically such that its arm A is towards left and arm B is towards right and the distance
AB is L. When it is at rest, a liquid stands at the same height is the two arms i.e., HA=HB. If the tube is
given an acceleration a towards right, then
(a)
(c)
HA=HB+ gL/a
HB=HA+ gL/a
(b)
(d)
HA =HB +aL/g
HB =HA +aL/g
Q.11
When an air bubble rises from the bottom of a lake to the surface, its radius doubles. If the atmospheric
pressure is equal to the column of water of height H. the depth of the lake is
(a)
H
(b)
2H
(c)
7H
(d)
8H
Q.12
A body is carrying a wood block weighing 0.1kg (density 500kg/m3) in his left-hand and a bucket partly
filled with water and weighing 10kg in his right-hand. The boy drops the block in water of bucket so that
the block starts floating. The load the boy is now carrying is
(a)
Aurora Classes
Properties of Matter
10kg
(b)
9.9kg
(c)
29
10.1kg
(d)
10.2kg
Q.13
Q.14
A body is partly floating in a liquid. The whole system falls freely under gravity. The up thrust on the
body due to the liquid is
(a)
zero
(b)
equal to weight of liquid displaced
(c)
equal to weight of the body in air
(d)
equal to weight of the immersed portion of the body.
A balloon filled with air is weighed so that it barely floats on water. When it is pushed down so that it
gets submerged a short distance in water than the balloon will
(a)
come up again to its former position
(b)
remain in the position where it is left
(c)
sink to the balloon
(d)
emerge on the liquid
*Q.15 A fluid is flowing through a pipe. Its cross - sectional area decrease from A1 and A2.
Q.16
(a)
If the fluid is non-compressible, the velocity increase in the ratio of A1/ A2
(b)
If the fluid is compressible, the velocity may remain constant provided its
density varies as 1/2 = A2/A1
(c)
If the fluid is non-compressible, its pressure increase as it enters into
narrower region
(d)
If the fluid is viscous, then Bernoulli’s theorem is not applicable but equation
of continuity still holds good
Water is floating through a system of two tubes joined one after the other. The radius of first tubes is
double that of the second tube, but the length of the two tubes are equal. Then if the pressure difference
across the first tube is p1 and across the second tube is p2 then
(a)
Q.17
Q.18
p2/p1=1
(b)
p2/p1=2
(c)
p2/p1=4
(d)
p2/p1=16
A small drop of water falls from rest through a great height h in air. The final velocity of drop is
(a)
almost independent of h
(c)
proportional to h
(b)
proportional to h
(d)
inversely proportional
A compressible fluid flows steadily through a pipe of cross-sectional area A1 and out of a narrowed
opening of area A2 = A1/5. If its density at a certain point P in the pipe is twice its density at the outlet Q
and if its speed at P is 2m/s, the speed at the outlet Q is
(a)
2m/s
(b)
5m/s
(c)
10m/s
(d)
20m/s
Aurora Classes
Properties of Matter
30
Q.19 A liquid can easily change its shape but a solid can not because
Q.20
(a)
the density of a liquid is smaller than that of a solid
(b)
the forces between the molecules is stronger in sold than in liquids
(c)
the atoms combine to form bigger molecules in a solid
(d)
the average separation between the molecules is larger in solids.
Consider the equations
P = Lim F/S and P1 – P2 = gz
In an elevator accelerating upward
(a)
both the equations are valid
(c)
the second is valid but not the first
Q.21
Q.22
Q.23
Q.24
Q.25
Q.26
Q.27
Q.28
Q.29
Q.30
(b)
(d)
the first is valid but not the second
both are invalid.
Equal mass of three liquids are kept in three identical cylindrical vessels A, B and C. The densities are A , B, c with A < B <
c. The force on the base will be
(a)
maximum in vessel A
(b)
maximum in vessel B
(c)
maximum in vessel C
(d)
equal in all the vessels.
A beaker containing a liquid is kept inside a big closed jar. If the air inside the jar is continuously pumped out, the pressure in
th4e liquid near the bottom of the liquid will
(a)
increase
(b)
decrease
(c)
remain constant
(d)
first decrease and then increase.
The pressure in a liquid at two points in the same horizontal plane are equal. Consider an elevator accelerating upward and a
car accelerating on a horizontal road. The above statements is correct in
(a)
the car only
(b)
the elevator only (c)
both of them
(d)
neither of them
Suppose the pressure at the surface of mercury in a barometer due is P 1 and the pressure at the surface of mercury in the cup
is P2.
(a)
P1 = 0, P2 = atmospheric pressure
(b)
P1 = atmospheric pressure, P2 = 0
(c)
P1 = P2 = atmospheric pressure
(d)
P1 = P2 = 0
A barometer kept in an elevator reads 76 cm when it is at rest. If the elevator goes up with increasing speed, the reading will
be
(a)
zero
(b)
76 cm
(c)
< 76 cm
(d)
> 76 cm.
A barometer kept in an elevator accelerating upward reads 76 cm. The air pressure in the elevator is
(a)
76 cm
(b)
< 76 cm
(c)
> 76 cm
(d)
zero.
To construct a barometer, a tube of length 1 m is filled completely with mercury and is inverted in a mercury cup. The
barometer reading on a particular day is 76 cm. Suppose a 1 m tube is filled with mercury up to 76 cm and then closed by a
cork. It is inverted in a mercury column in the tube over the surface in the cup will be
(a)
zero
(b)
76 cm
(c)
>76 cm
(d)
< 76 cm.
A 20 N metal block is suspended by a spring balance. A beaker containing some water is placed on a weighing machine
which reads 40 N. The spring balance is now lowered so that the block gets immersed in the water. The spring balance now
reads 16 N. The reading of the weighing machine will be
(a)
36 N
(b)
60 N
(c)
44 N
(d)
56 N.
A piece of wood is floating in water kept in a bottle. The bottle is connected to an air pump. Neglect the compressibility of
water. When more air is pushed into the bottle from the pump, the piece of wood will float with
(a)
larger part in the water
(b)
lesser part in the water
(c)
same part in the water
(d)
it will sink.
A metal cube is placed in an empty vessel. When water is filled in the vessel so that the cube is completely immersed in the
water, the force on the bottom of the vessel in contact with the cube
(a)
will increase
(b)
will decrease
(c)
will remain the same
(d)
will become zero.
1
Q.31
Q.32
Q.33
Q.34
Q.35
Q.36
Q.37
A closed cubical box is completely filled with water and is accelerated horizontally towards right with an acceleration a. The
resultant normal force by the water on the top of the box
(a)
passes through the center of the top
(b)
passes through a point to the right of the center
(c)
passes through a point to the left of the center
(d)
becomes zero.
Consider the situation of the previous problem. Let the water push the left wall by a force F 1 and the right wall by a force F2.
(a)
F1 = F2
(b)
F1 > F2
(c)
F1 < F2
(d)
The information is insufficient to know the relation between F 1 and F2.
Water enters through end A with a speed v1 and leaves through end B with a speed v2 of a cylindrical tube AB. The tube is
always completely filled with water. In case I the tube is horizontal, in case II it is vertical with the end A upward and in case
III it is vertical with the end B upward. We have v1 = v2 for
(a)
case I
(b)
case II
(c)
case III
(d)
each case.
Bernoulli’s theorem is based on conservation of
(a)
momentum
(b)
mass
(c)
energy
(d)
angular momentum.
Water is flowing through a long horizontal tube. Let P A and PB be the pressures at two points A and B of the tube.
(a)
PA must be equal to PB.
(b)
PA must be greater than PB.
(c)
PA must be smaller than PB.
(d)
PA = PB only if the cross-sectional area at A and B are equal.
Water and mercury are filled in two cylindrical vessels up to same height. Both vessels have a hole in the wall near the
bottom. The velocity of water and mercury coming out of the holes are v 1 and v2 respectively.
(a)
v1 = v2
(b)
v1 = 13.6 v2
(c)
v1 = v2/13.6
(d)
v1 = 13.6 v2.
A larger cylindrical tank has a hole of area A its bottom. Water is poured in the tank by a tube of equal cross-sectional area A
ejecting water at the speed v.
(a)
The water level in the tank will keep on rising.
(b)
No water can be stored in the tank.
(c)
The water level will rise to height v2/2g and then stop.
(d)
The water level will oscillate.
Q.38 A rope 1 cm in diameter breaks if the tension in it exceeds 500 N. The maximum tension that may be
given to a similar rope of diameter 2 cm is
Q.39
Q.40
Q.41
Q.42
(a)
500 N
(b)
250 N
(c)
1000 N
(d)
2000 N.
The breaking stress of wire depends on
(a)
material of the wire
(b)
length of the wire
(c)
radius of the wire
(d)
shape of the cross-section.
A wire can sustain the weight of 20 kg before braking . If the wire is cut into two equal parts, each part can sustain a weight
(a)
10 kg
(b)
20 kg
(c)
40 kg
(d)
80 kg.
Two wires A and B are made of same material. The wire A has a length l and diameter r while the wire B has a length 2l and
diameter r/2. If the two wires are stretched by the same force, the elongation in A divided by the elongation in B is
(a)
1/8
(b)
¼
(c)
4
(d)
8.
A wire elongates by 1.0 mm when a load W is hanged from it. If this wire goes over a pulley and two weights W each are
hung at the two ends, the elongation of the wire will be
(a)
0.5 m
(b)
1.0 mm
(c)
2.0 mm
(d)
4.0 mm.
2
Q.43
A heavy uniform rod is hanging vertically from a fixed support. It is stretched by its own weight. The diameter of the rod is
(a)
smallest at the top and gradually increases down the rod
(b)
largest at the top and gradually decreases down the rod
(c)
uniform everywhere
(d)
maximum in the middle.
Q.44
When a metal wire is stretched by a load, the fractional change in its volume V/V is proportional to
Q.45
(a)
l/ l
(b)
(l/l)2
(c)
l/l
(d)
none of these.
The length of a metal wire is l1 when the tension in it is T1 and is l2 when the tension is T2. The natural length of the wire is
Q.46
Q.47
Q.48
Q.49
Q.50
Q.51
(a)
l1 + l2 /2
(b)
l1 l2
(c)
l1T2 - l2T1/T2 – T1
(d)
l1T2 + l2T1/T2 + T1.
A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break
(a)
when the mass is at the highest point
(b)
when the mass is at the lowest point
(c)
when the wire is horizontal
(d)
at an angle of cos-1 (1/3) from the upward vertical.
When a metal wire elongates by hanging a load on it, the gravitational potential energy is decreased.
(a)
This energy completely appears as the increased kinetic energy of the block.
(b)
This energy completely appears as the increased elastic potential energy of the wire.
(c)
This energy completely appears as heat.
(d)
None of these.
By a surface of a liquid we mean
(a)
geometrical plane like x = 0
(b)
all molecules exposed to the atmosphere
(c)
a layer of thickness of the order of 10 -8 m
(d)
a layer of thickness of the order of 10 -4 m.
An ice cube is suspended in vacuum in a gravity free hall. As the ice melts it
(a)
will retain its cubical shape
(b)
will change its shape to spherical
(c)
will fall down on the floor of the hall
(d)
will fly up.
When water droplets merge to form a bigger drop
(a)
energy is liberated
(b)
surface tension
(c)
energy is neither liberated nor absorbed
(e)
energy may either be liberated or absorbed depending on the nature of the liquid.
-1 -2
The diameter ML T can correspond to
(a)
moment of force
(b)
surface tension
(c)
modulus of elasticity
(d)
coefficient of viscosity.
Q.52
Air is pushed into a soap bubble of radius r to double its radius. If the surface tension of the soap solution is S, the
work done in the process is
(a)
8r2S
(b)
12 r2S
(c)
16  r2S
(d)
24  r2S.
Q.53
If more air is pushed in a soap bubble, the pressure in it
(a)
decreases
(b)
increases
(c)
remains same
(d)
becomes zero.
If two soap bubbles of different radii are connected by a tube,
(a)
air flows from bigger bubble to the smaller bubble till the sizes become equal
(b)
air flows from bigger bubble to the smaller bubble till the sizes are interchanged
(c)
air flows from the smaller bubble to the bigger
Q.54
3
Q.55
Q.56
Q.57
Q.58
Q.59
Q.60
Q.61
Q.62
Q.63
(d)
there is no flow of air.
The excess pressure inside a soap bubble is twice the excess pressure inside a second soap bubble. The volume of the first
bubble is n time the volume of the second where n is
(a)
4
(b)
2
(c)
1
(d)
0.125.
Water rises in a vertical capillary tube upto a length of 10 cm. If the tube is inclined at 45, the length of water risen in the
tube will be
(a)
10 cm
(b)
102 cm
(c)
10/2 cm
(d)
none of these.
A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling
elevator, the length of water column in the capillary tube will be
(a)
8 cm
(b)
6 cm
(c)
10 cm
(d)
20 cm.
viscosity is a property of
(a)
liquids only
(b)
solids only
(c)
solids and liquids only
(d)
liquids and gases only.
The force of viscosity is
(a)
electromagnetic
(b)
gravitational
(c)
nuclear
(d)
weak.
The viscous force acting between two layers of a liquid is given by F/A = -  dv/dz This F/A may be called
(a)
pressure
(b)
longitudinal stress
(c)
tangential stress
(d)
volume stress.
A raindrop falls near the surface of the earth with almost uniform velocity because
(a)
its weight is negligible
(b)
the force of surface tension balances its weight
(c)
the force of viscosity of air balances its weight
(d)
the drops are charged and atmospheric electric field balances its weight.
A piece of wood is taken deep inside a long column of water and released. It will move up
(a)
with a constant upward acceleration
(b)
with a decreasing upward acceleration
(c)
with a deceleration
(d)
with a uniform velocity
A solid sphere falls with a terminal velocity of 20 m/s in air. If it is allowed to fall in vacuum,
(a)
terminal velocity will be 20 m/s
(b)
terminal velocity will be less than 20 m/s
(c)
terminal velocity will be more than 20 m/s
(d)
there will be no terminal velocity.
4
ANSWER SHEET
1.
(a)
2.
(d)
3.
(d)
4.
(c)
5.
(c)
6.
(a)
7.
(c)
8.
(b)
9.
(a)
10.
(b)
11.
(c)
12.
(c)
13.
(a)
14.
(c)
15.
(a), (b), (d)
16.
(d)
17.
(a)
18.
(d)
19.
(b)
20.
(b)
21.
(d)
22.
(b)
23.
(b)
24.
(a)
25.
(c)
26.
(c)
27.
(d)
28.
(c)
29.
(c)
30.
(c)
31.
(d)
32.
(b)
33.
(d)
34.
(c)
35.
(d)
36.
(a)
37.
(c)
38.
(d)
39.
(a)
40.
(b)
41.
(a)
42.
(b)
43.
(a)
44.
(a)
45.
(c)
46.
(b)
47.
(d)
48.
(c)
49.
(b)
50.
(a)
51.
(c)
52.
(d)
53.
(a)
54.
(c)
55.
(d)
56.
(b)
57.
(d)
58.
(d)
59.
(a)
60.
(c)
61.
(c)
62.
(b)
63.
(d)
5
SURFACE TENSON
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
A bubble of 8 mm diameter is formed in the air. The surface tension of soap solution is 30 dyne/cm. The excess
pressure inside the bubble is
(a)
150 dyne/cm2
(b)
300 dyne/cm2
-3
2
(c)
3  10 dyne/cm
(d)
12 dyne/cm2
-1
The surface tension of a liquid is 5 Nm . If a thin film is formed on a loop of area 0.02 m2, then its surface energy
will be
(a)
5  10-2 J
(b)
2.5  10-2 J
(c)
2  10-2 J
(d)
3  10-1 J
The excess pressure inside an air bubble of radius r, which is inside a liquid of surface tension  is
(a)
2/r
(b)
/r
(c)
4/r
(d)
zero.
A capillary tube made of glass is dipped into mercury.
(a) mercury rise in the capillary tube
(b) mercury rises and flows out of the capillary tube
(c) mercury descends in the capillary tube
(d) mercury neither rises nor descends in the capillary tube.
Two tubes of same material but of different radii are dipped in a liquid. The height to which a liquid rises in one
tube is 2.2 cm and in the other is 6.6 cm. The ratio of their radii is
(a)
9:1
(b)
1:9
(c)
3:1
(d)
1:3
Two soap bubbles, each with a radius r, coalesce in vacuum under isothermal conditions to form a bigger bubble of
radius R. Then R is equal to
(a)
2-1/2r
(b)
21/3r
(c)
21/2r
(d)
2r.
A liquid tens to assume a spherical shape because of
(a)
the surface tension force
(b)
the viscous force
(c)
the gravity effect
(d)
the elastic force.
The meniscus of mercury in the glass capillary tube is
(a)
convex
(b)
concave
(c)
plane
(d)
uncertain.
It is difficult to write legibly with a fountain pen on a newspaper because of
(a)
inertia
(b)
capillary action (c)
elasticity(d)
surface tension.
The potential energy of a molecule on the surface of a liquid compared to one inside the liquid is
(a)
zero
(b)
smaller
(c)
the same
(d)
greater.
The angle of contact between a solid and a liquid is a characteristic property of
(a)
solid only
(b)
liquid only
(c)
both the solid and liquid
(d)
shape of the solid.
The area enclosed by a thread of a given perimeter is maximum when its shape is a
(a)
Square
(b)
Rectangle
(c)
Circle
(d)
Ellipse.
Two water drops, each of radius r coalesce to from a bigger drop of radius R. Then R is equal to
(a)
2-1/2r
(b)
21/3r
(c)
21/3r
(d)
2r.
If FC and FA denote cohesive and adhesive force on a liquid molecule near the surface of a solid, then the surface of
liquid is convex if
(a)
FA > FC/2
(b)
FA = FC/2
(c)
FA < FC/2
(d)
FA < FC.
A liquid will rise in a capillary tube if the angle of contact is
(a)
< 90
(b)
> 90
(c)
- 90
(d)
90.
The surface area of a body of given volume is least when its shape is
(a)
cubic
(b)
ellipsoidal
(c)
paraboloidal
(d)
spherical.
Water rises to a height of 10 cm in a glass capillary tube. If the area of cross-section of the tube is reduced to one
fourth of the former value, the water will rise to
(a)
20 cm
(b)
5 cm
(c)
2.5 cm
(d)
40 cm
A liquid is contained in a vessel. The liquid-solid adhesive force is very weak as compared to the cohesive force in
the liquid. The shape of the liquid surface will be
(a)
horizontal
(b)
vertical
(c)
concave
(d)
convex
1
19.
Two liquids drops coalesce to form a large drop. Now,
(a)
energy is liberated
(b)
energy is neither liberated nor absorbed
(c)
some mass gets converted into energy (d)
energy is absorbed.
The lower end of a capillary tube is at a depth of 12 cm and the water rises 3cm in it. The mouth pressure required to
blow an air bubble at the lower end will be x cm of water column, where x is
(a)
12
(b)
15
(c)
3
(d)
9
The addition of soap changes the surface tension of water to
(a)
1 > 2
(b)
1 < 2
(c)
1 = 2
(d)
it is not possible to predict the above.
The term ‘surface of a liquid’ means
(a) a layer of thickness of the order of 10-8 m (b)
a geometrically plane surface of the liquid
(b) an assembly of molecules exposed to air (d)
a group of molecules on the surfaces of a liquid.
Water rises in a vertical glass capillary tube up to a length of 8 cm. If the tube is inclined at 45, the length of water
column in the tube will be
(a)
4 cm
(b)
3 dm
(c)
82 cm
(d)
8/2 cm
Water rises in a capillary tube up to a height h. Water wets the tube completely. The tube is gradually depressed into
the water. The height at which the surface becomes flat is
(a)
h/2
(b)
3h/4
(c)
h/4
(d)
zero.
A number of droplets, each of radius r, combine to form a drop of radius R. If T is the surface tension, then the rise
in temperature will be
(a)
2T/r
(b)
3T/R
(c)
2T [1/r – 1/R]
(d)
3T [1/r – 1/R].
The amount of work done in increasing size of soap film 6 cm  4 cm to 12 cm  8 cm is (surface tension 30 dyne
/cm)
(a)
2160 erg
(b)
4320 erg
(c)
720 erg
(d)
1440 erg
The amount of work done in forming a soap film of size tube 10 cm  10 cm is
(a)
6  10-4 J
(b)
3  10-4 J
(c)
2  10-3 J
(d)
3  10-2 J
When two soap bubbles of radii r1 and r2 (r2 > r1) coalesce, the radius of curvature of common surface is
(a)
r2 – r1
(b)
r2 – r1/ r1r2
(c)
r1 r2/ r2 – r1
(d)
r2 + r 1
If work W is done in blowing a bubble of radius R from a soap solution, then the work done in blowing a bubble of
radius 2R from the same solution is
(a)
W/2
(b)
2W
(c)
4W
(d)
21/3 W.
The surface tension of a soap solution is 2  10-2 Nm-1. To blow a bubble of radius 1 cm, the work required to be
done is
(a)
4  10-6 J
(b)
8  10-6 J
(c)
12  10-6 J
(d)
16  10-6 J
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
ANSWER SHEET
1.
(b)
2.
(c)
3.
(a)
4.
(c)
5.
(c)
6.
(c)
7.
(a)
8.
(a)
9.
(b)
10.
(d)
11.
(c)
12.
(c)
13.
(b)
14.
(c)
15.
(a)
16.
(d)
17.
(a)
18.
(d)
19.
(a)
20.
(b)
21.
(b)
22.
(a)
23.
(c)
24.
(d)
25.
(d)
26.
(b)
27.
(a)
28.
(c)
29
(c)
30.
(d)
2
SHM
Q.1
Q.2
Q.3
The maximum speed of a particle of mass 0.2kg executing SHM is 1.57m/s and maximum
acceleration is 2.465m/s2. Then
(a)
Its angular frequency is 1/1.57 rad/s
(b)
Its time period is 4s
(c)
Its amplitude is 0.1m
(d)
Its total energy is 0.25J
The displacement of a particle of mass 0.1 kg executing SHM is given by y =5sin 200t where
distance are in cm and time in s.
(a)
Maximum velocity is 10m/s.
(b)
Acceleration at y = 2.5cm is –103m/s2
(c)
Restoring force when at one extremity is 100N
(d)
Time period of oscillatic is /100s.
The displacement of a particle from its mean position is given by the equation
Y=0.4(cos2t/2-sin2t/2)
Q.4
Q.5
Q.6
Q.7
(a)
The motion of particle is not SHM
(b)
The motion is SHM with a period of 2s
(c)
The amplitude of SHM is 0.4m
(d)
The maximum velocity is 0.4m/s.
The total energy of a simple pendulum executing SHM with amplitude A is E. When its displacement
is half the amplitude, then
(a)
its KE is ½ E
(b)
its PE is ½ E
(c)
its PE is ¼ E and KE is ¾ E
(d)
its restoring force is E/A.
For a particle executing SHM, the kinetic energy varies as K = K0 cos2 t
(a)
(b)
The maximum kinetic energy is K0
he maximum potential energy is K0
(c)
The total mechanical energy is 2K0
(d)
The frequency with which KE varies is 2.
Which of the following does represent SHM ?
(a)
sin t + sin 2t
(b)
tan t
(c)
sin t + cos t
(d)
none of the above
A particle moving with SHM passes through points A and B with the same velocity. It takes 2s in
going from A to B and after another 2s, it again returns to B. The period in seconds of motion is
(a)
Q.8
Q.9
2
(b)
4
(c)
6
(d)
8
A linear harmonic oscillator of force constant 2  10 N/m and amplitude 0.01m has a total
mechanical energy of 160J. Its
6
(a)
maximum potential energy is 100J
(b)
maximum kinetic energy is 100J
(c)
maximum potential energy is160J
(d)
maximum potential energy is zero
Two particle are oscillating along the same line with the same frequency and same amplitude. They
meet each other at points mid-way between the mean position and extreme position while going in
opposite directions. The phase difference between their motions is
(a)
Aurora Classes
/3
(b)
/2
(c)
3
2/3
(d)
5/4
Crash Course
Q.10
Q.11
Q.12
Q.13
Q.14
Q.15
Q.16
Q.17
Q.18
Q.19
Q.20
Q.21
Q.22
Two pendulums have the time periods T and 5T/4. They start SHM at the same time from the mean
position. After hoe many oscillations of the smaller pendulum they will be again in the same phase
(a)
5
(b)
4
(c)
11
(d)
9
Two pendulum of period T and 4T are given small displacements in the same direction at the same
instant. They will be out of phase after the shorter pendulum has completed n oscillations where n is
(a)
2/3
(b)
4/3
(c)
3
(d)
5
The length of a simple pendulum is infinite. Its time period T in terms of radius R of the earth is
(a)
2R/g
(b)
2R/2g
(c)
22R/g
(d)
infinite
A simple pendulum of length l has been set up inside a railway wagon sliding down a frictionless
inclined plane having an angle of inclination  with the horizontal. What will be its period of
oscillation as recorded by an observer inside the wagon?
(a)
2 l/g cos 
(b)
2 l/g sin 
(c)
2 l/g
(d)
2l cos/g
A simple pendulum has time period given by T = 2l/g. If it is falling down with its support with
acceleration a, its new time period T’ is
(a)
T’ = 2l/g
(b)
T’ = 2l / (g-a)
(c)
T’ = 2l / (g+a)
(d)
It will not oscillate at all.
A simple pendulum with metal bob has a period T. The metal bob is non-immersed in a liquid having
density 1/10 that of the metal of the bob. The liquid is non-viscous. Now the period of the same
pendulum with its bob remaining all the time in the liquid will be
(a)
9/10T
(b)
T10/9
(c)
T
(d)
T9/10
A heavy brass-sphere is hung from a spiral spring and it executes vertical vibrations with period T.
The ball is now immersed in non-viscous liquid with a density 1/10 that of brass. When set into
vertical vibrations with the sphere remaining inside the liquid all the time, the period will be
(a)
9/10T
(b)
T10/9
(c)
T
(d)
T9/10
Two spring of the same material but of length L and 2L are suspended with masses. M and 2M
attached at their lower ends. Their times periods when they are allowed to oscillate will be in the
ratio
(a)
1:2
(b)
2:1
(c)
1:4
(d)
4:1
Masses M and 4M are suspended from two identical springs of the same spring constant k. They start
oscillating in the same phase and they are again in the same phase after every 4 seconds. If M = 1kg,
the value of k is N/m is
(a)

(b)
2
(c)
2
(d)
4
A simple spring has length l and force constant k. It is cut into parts of lengths l1 and l2 such that l1=
nl2 (n= an integer). The force constant of spring of length l1 is
(a)
k(1+n)
(b)
k/n (1+n)
(c)
k
(d)
k/n
A block of mass m is attached to two springs as shown in Fig. 12-28, with spring constant k and 2k.
The mass oscillates with an amplitude A.
(a)
The angular frequency of oscillation is 2k/3m
(b)
The maximum energy of oscillation is 3/2 kA2
(c)
The maximum restoring force is 3k A/m.
(d)
The maximum velocity of oscillation is Ak/m
A body of mass m is suspended from a spring of force constant k. The maximum distance upto which
the body can be pulled down for the oscillation to remain harmonic is
(a)
2mg/k
(b)
mg/k
(c)
2k/mg
(d)
k/mg
One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to massless
spring of spring constant k. A mass m hangs freely from the free end of the spring. The area of crosssection and Young’s modules of the wire are A and Y respectively. If the mass is slightly pulled
down and released, it will oscillate with a time period T equal to
(a)
2m/k
(b)
2m(YA+kL)/YAk
(c)
2mYA/kL
(d)
2mL/YA
Aurora Classes
4
Crash Course
Q.23
A frictionless piston of mass M is just fit in the vertical cylindrical neck of a large container of
volume V. The container is filled with a gas and there is a vacuum above the piston. Assuming
Boyle’s law, the time period T of oscillation will be
(a)
TM1/2
(b)
TM-1/2
(c)
TM0
(d)
TM
Q.24 A uniform cylinder of length L and mass M having cross sectional area A is suspended with its length
vertical from fixed point by a massless spring such that it is half submerged in a liquid of density  at
equilibrium position. When the cylinder is given a small downwards push and released it starts
oscillating vertically with small amplitude. If the force constant of the spring is k, the frequency of
oscillation of the cylinder is
(a)
1/2[k-Ag/M]1/2
(b)
1/2[k+Ag/M]1/2
2
1/2
(c)
1/2[k-gL /M]
(d)
1/2[k-Ag/Ag ]1/2
Q.25 Consider three u-tubes containing the same liquid. The radii and length of the horizontal tube are
related as follows:
r1 = r,
r2 = 2r
r3 = r
l1 = l,
l2 = l
l3 = 3l
and they are filled up to the same height h. When the liquid is disturbed, it oscillates in simple
harmonic motion with periods T1, T2 and T3, then
(a)
T1< T2< T3
(b)
T1= T2> T3
(c)
T1= T2< T3
(d)
T2< T1< T3
Q.26 A bottom loaded stick performs SHM in a liquid of density 1with time period T1 and in a liquid of density 2
with time period T2. If the lengths insides the two liquids are l1 and l2 respectively, then
(a)
l11/l22
(b)
l21/l12
(c)
T11 = T22
(d)
T22 = T11
ANSWER SHEET
1.
(b), (d)
2.
(a),(b), (c)
3.
(b), (c), (d)
4.
(c), (d)
6.
(c)
7.
(d)
8.
(b), (c)
9.
(c)
10.
(a)
11.
(a)
12.
(a)
13.
(a)
14.
(b)
15.
(b)
16.
(c)
17.
(a)
18.
(b)
19.
(b)
20.
(b), (c)
21.
(b)
22.
(b)
23.
(c)
24.
(b)
25.
(c)
26.
(a), (d)
Aurora Classes
5
5.
(a), (b), (d)
Crash Course
Heat
Kinetic Theory of Gases-Laws
Q.1
Two gasses X and Y having the same temperature T, same pressure p and same volume V are mixed. If the mixture is at the
same temperature T and occupies the same volume V, the pressure of the mixture is
(a)
Q.2
Q.3
p/2
(d)
4/p
(b)
twice that of helium
(c)
half that of helium
(d)
2 times that of helium
The molecules of a given mass of an ideal gas have rms speed of 300m/s at 37C and 2  105 Pa. When the temperature is
967C and the pressure is 6105Pa, the rms value in m/s is
6003
(b)
6002
(c)
600
(d)
1200
The rms speed of the molecules of hydrogen at 27 C is v1 and the rms speed of oxygen at 402C is v2, then
3v1 = 8v2
(b)
8v1 = 3v2
(c)
9v1 = 4v2
(d)
4v1 = 9v2
At identical temperatures, the rms speed of hydrogen molecules is 4 times that for oxygen molecules. In a mixture the two
gases are present in the mass ratio of 1:8 respectively. The rms speed of all molecules of the mixture is n times the rms speed
for oxygen molecules, where n is
3
(b)
4/3
(c)
(8/3)1/2
(11)1/2
(d)
At room temperature the rms speed of the molecules of a certain diatomic gas is found to be 1930m/s. The gas is
(a)
Q.7
(c)
equal to that of helium
(a)
Q.6
p
(a)
(a)
Q.5
(b)
Two vessels having equal volume contain molecular hydrogen at one atmosphere and helium at two atmosphere respectively.
If both samples are at the same temperature, the rms speed of hydrogen molecules is
(a)
Q.4
2p
H2
(b)
F2
(c)
O2
(d)
C12
Three closed vessels A,B and C are at the same temperature and contain gases which obey Maxwellian distribution of
velocities. Vessels A contains only O2, B only N2 and C a mixture of equal quantities of O2 and N2. If the average speed of
O2 molecules in vessels A is v1 that of the N2 molecules in vessel B is v2, the average speed of the O2 molecules in vessel C is
(a)
(v1 + v2)1/2
(b)
v1
(c)
(v1 v2)1/2
3kT/M
(d)
where M is the mass of an oxygen molecule.
*Q.8
Q.9
A mixture of two gases A and B is in thermal equilibrium
(a)
the rms speed of the molecules-A is equal to the rms speed of the molecules-B.
(b)
the average kinetic energy of molecules-A is equal to the average kinetic energy of molecules-B.
(c)
the heavier molecules move with smaller rms speed but average kinetic energy of heavier molecules is
same as that of lighter molecules.
(d)
the heavier molecules move with smaller rms speed and they have a small average kinetic energy than
those of lighter molecules.
The energy of a gas per liter is 300J, then its pressure in N/m 2 will be
(a)
Q.10
(c)
105
(d)
2  105
1:1
(b)
1:2
(c)
2:1
(d)
1 : 16
127C
(b)
527C
(c)
-73C
(d)
-173C
The kinetic energy of oxygen at-23C and 60cm pressure is 120J, when its volume is one liter. The kinetic energy of
hydrogen having volume one liter, temperature 227C and pressure 120 cm will be
(a)
Q.13
6  105
At what temperature, the mean kinetic energy of O2 will be same for H2 molecules at- 73C
(a)
Q.12
(b)
If the number of molecules of H2 are double than that of O2, then ratio of average kinetic energy of hydrogen and that of
oxygen, both at 300 K is
(a)
Q.11
3  105
480J
(b)
960J
(c)
240J
(d)
120J
A box containing N molecules of a perfect gas at temperature T1 and pressure p1. The number of molecules in the box is
doubled keeping the mean energy of the gas same as before. If the new pressure is p2 and temperature T2, then
Aurora Classes
2
Kinetic Theory of Gases
(a)
Q.14
p2 = p1, T2 = T1
(b)
p2 = p1, T2 = T1/2 (c)
p2 = 2p1, T2 = T1 (d)
p2 = 2p1, T2 = T1/2
A box containing N molecules of a perfect gas at temperature T1 and pressure p1. The number of molecules in the box is
doubled, keeping the total kinetic energy of the gas same as before. If the new pressure is p2 and temperature T2, then
(a)
p2 = p1, T2 = T1
(c)
p2 = 2p1, T2 = T1
(b)
p2 = p1, T2 = T1/2
(d)
p2 = 2p1, T2 = T1/2.
2
Q.15
An ideal gas is found to obey an additional law Vp = constant. The gas is initially at temperature T and volume V. When it
expands to a volume 2V, the temperature becomes
Q.16
An ideal gas expands in such a manner that its pressure and volume comply with the condition pV2 = constant. During this
process, the gas is
(a)
Q.17
T2
(b)
2T
(c)
T/2
(d)
4T
(a)
heated
(b)
cooled
(c)
neither heated not cooled
(d)
first heated and then cooled.
Two jars A and B contains Helium and Oxygen at the same temperature and at pressure of 1 atm and 4 atm respectively. If E1
and E2 be the average kinetic energy of translation per per molecule of each gas then
(a)
E1 = 8 E 2
(b)
E2 = 8 E 1
(c)
ANSWER SHEET ( Kinetic
E1 = E 2
(d)
E1 = 4 E 2
Theory of Gases)
1.
(a)
2.
(d)
3.
(c)
4.
(a)
5
(d)
6.
(a)
7.
(b)
8.
(b), (c)
9.
(d)
10.
(a)
11.
(c)
12.
(c)
13.
(c)
14.
(b)
15.
(a)
16.
(b)
17.
(c)
2
Thermal Expansion
(Objective Question)
*Q.1
Q.2
A hollow copper cylinder is heated, then its
(a)
internal diameter decreases
(b)
external diameter increases
(c)
volume of metal increases
(d)
density of material decreases.
Two rods of different materials having co-efficient of thermal expansion 1, 2 and Young’s modulii Y1, Y2
respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same
increase in temperature. There is no bending of the rods. If 1 : 2 = 2 : 3, the thermal stress developed in the two
rods are equal provided Y1 : Y2 is equal to
(a)
*Q.3
Q.4
Q.5
Q.6
Q.8
Q.9
(b)
1:1
(c)
3:2
(d)
4:9
A metallic circular disc having a circular hole at its centre is rotating about an axis passing through its centre and
perpendicular to its plane. When the disc is heated
(a)
the speed of disc increases
(b)
the diameter of hole decreases
(c)
the moment of inertia of disc increases
(d)
the speed of disc decreases
A crystal has a co-efficient of liner expansion 12  10-7/C in one direction and 213  10-7/C in every direction at
right angles to it. The co-efficient of cubical expansion of the crystal is
(a)
36  10-7/C
(b)
639  10-7/C
(c)
273  10-7/C
(d)
438  10-7/C
A metallic hollow sphere of negligible co-efficient of cubic expansion just floats in water at 4C. If the water is (i)
heated to 6C, (ii) cooled to 2C, then
(a)
sphere sinks in both cases (i) and (ii)
(b)
sphere floats in both cases (i) and (ii)
(c)
sphere sinks in both case (i) but floats in case (ii)
(d)
sphere floats in both cases (i) but sinks in case (ii)
A metal ball immersed in alcohol weighs W1 at 0C and W2 at 59C. The co-efficient of cubical expansion of the
metal is less than that of the alcohol. Assuming that the density of the metal is large compared to that of alcohol, it
can be shown that
(a)
Q.7
2:3
W1 > W2
(b)
W1 = W2
(c)
W1 < W2
(d)
W2 = (W1/2)
A block of wood is floating on water at 0C with certain volume v above water. The temperature of water is
slowly raised from 0C to 15C, then the volume v will
(a)
remain unchanged
(b)
decrease
(c)
first increase then decrease
(d)
first decrease then increase
In the previous question, the distance between the holes will
(a)
increase
(b)
decrease
(c)
remain constant
(c)
may either increases or decrease depending on the positions of the holes on the sheet and on the
ratio d1/d2.
A metal wire of length  and area of cross-section A is fixed between rigid supports at negligible tension. If this is
cooled, the tension in the wire will be
(a)
proportional to 
(b)
inversely proportional to 
(c)
independent of 
(d)
independent of A
3
Q.10
Two metal rods of the same length and area of cross-section are fixed end to end between rigid supports. The
materials of the rods have Young modulii Y1 and Y2, and coefficients of linear expansion 1 and 2. The junction
between the rods does not shift if the rods are cooled
(a)
Q.11
Y11 =Y22
(b)
Y12 =Y21
(c)
Y121 =Y222
(d)
Y121 =Y222
When the temperature of a body increases from t to t +∆t, its moment of inertia increases from I to I + ∆I. The
coefficient of linear expansion of the body is . The ratio ∆I/I is equal to
Q.12
Q.13
(a)
∆t/t
(b)
2∆t/t
(c)
∆t
(d)
2∆t
A horizontal tube, open at both ends, contains a column of liquid. The length of this liquid column does not
change with temperature. Let  = coefficient of volume expansion of the liquid and  = coefficient of linear
expansion of the martial of the tube
(a)

(c)


(d)

f1-f2 /f2t1-f1t2
(b)
f1-f2/f1t1-f2t2
(c)
f1+f2/f2t1+f1t2
(d)
f1+f2/f1t1+f2t2
A solid with coefficient of linear expansion  just floats in a liquid whose coefficient of volume expansion is
heated, the solid will
(a)
sink in all causes
(b)
continue to float in all cases
(c)
Q.15
b)
A solid whose volume does not change with temperature floats in a liquid. For two different temperature t 1 and t2
of the liquid, frictions f1 and f2 of the volume of the solid remain submerged in the liquid. The coefficient of
volume expansion of the liquid is equal to
(a)
Q.14

sink if  > 3
(d)
sink if  < 3 
The moment of inertia of a body is I and the linear coefficient of expansion is  If the temperature rises by a
small amount , then the change in the moment of inertia is approximately
(a)
 I ()
(b)
2  I ()
(c)
4  I ()
(d)
 I ()/2
*Q.16 A bimetallic strip is formed out of two identical strips, one of copper and the other of brass. The coefficients of
linear expansion of two metals are c and B. On heating, the temperature of the strip goes up by T and the strip
bends to form an are of circle of radius R. Then R is
(a)
proportional to T
(b)
inversely proportional to T
(b)
proportional to | A- B |
(d)
inversely proportional to | A- C |
*Q.17 The temperature of an isotropic cubical solid of length L, density d and coefficient of linear expansion per
Kelvin is raised by 10C, then at this temperature to a good approximation
Q.18
(a)
length is L (1 + 10 )
(b)
total surface area is L (1 + 2)
(c)
density is d (1 + 30 )
(d)
density is d/ (1 + 30 )
Two rods of lengths l1 (aluminimum) and l2 (steel having thermal coefficient of linear expansion A and s
respectively are connected end-to-end. Change in temperature T produces equal changes in their lengths. The
ratio l1/(l1 + l2) is
(a)
A/ S
(b)
A/ (AS)
(c)
S/ (AS)
(d)
S/ A
2
ANSWER SHEET
Thermal Expansion
1.
(b), (c), (d)
2.
(c)
3.
(c), (d)
4.
(d)
5.
(a)
6.
(c)
7.
(c)
10.
(a)
8.
(a)
9.
(c)
11.
(d)
12.
(b)
13.
(a)
14.
(c)
15.
(b)
16.
(b), (d)
17.
(a), (d)
18.
(c)
3
Thermal Conduction & Radiation
Q.1
Q.2
Q.3
Q.4
Q.5
Q.6
Q.7
Q.8
Q.9
Q.10
Q.11
Two identical vessels A and B having the same thickness of walls, but their thermal conductivities are KA and KB.
Both are filled with the same quantity of ice. If the time taken for melting the ice fully is 20 s and 30 s
respectively, then the ratio KA and KB will be
(a)
4:9
(b)
2:3
(c)
3:2
(d)
9:4
Two rods A and B are of equal lengths. Their ends are kept between the same temperature and their area of cross –
sections are A1 and A2 and thermal conductivities k1 and k2. The rate of heat transmission in the two rods will be
equal, if
(a)
k1 A2 = k2 A1
(b)
k1 A1 = k2 A2
(c)
k1 = k2
(d)
k1 A12 = k2 A22
Wires A and B have identical lengths and have circular cross sections. The radius of A is twice the radius of B
i.e,RA = 2RB. For a given temperature difference between the two ends, both wires conduct heat at the same rate.
The relation between the thermal conductivities is given by
(a)
kA = 4kB
(b)
kA = 2kB
(c)
kA = kB/2
(d)
kA = kB/4
Two identical plates of different metals as joined to form a single plate whose thickness of each plate. If the coefficients of conductivity of each plate are 2 and 3 units respectively, then the conductivity of the composite plate
will be
(a)
5
(b)
2.4
(c)
1.5
(d)
1.2
A wall has two layers A and B, each made of different materials. Both the layers have the same thickness. The
thermal conductivity of the material A is twice that of B. Under thermal equilibrium, the temperature difference
across the wall is 36C. The temperature difference across the layer A is
(a)
6C
(b)
12C
(c)
8C
(d)
24C
A cylinder of radius R made of a material of thermal conductivity k1 is surrounded by a cylindrical shell of inner
radius R and outer radius 2R made of a material of thermal conductivity k2. The two ends of the combined system
are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system
is in steady state. The effective thermal conductivity of the system is
(a)
k1 + k2
(b)
k1 k2/ (k1 + k2) (c)
k1 + 3k2) /4
(d)
(3 k1 + k2) /4
Two different metallic rectangular blocks A and have the same cross section and length. They are kept in contact
with their cross sections together. One end of block A is at temperature 100C while the far end of blocks B is at
0C. If the condctivity co – efficient of A and B are in the ratio 1:3, the temperature of the junction in the steady
state is
(a)
25C
(b)
50C
(c)
75C
(d)
100C
The thermal conductivity of a metal is 1600 W/m.K. In the steady state the temperature gradient which will
transmit 400103 W/m2 of heat energy should be
(a)
100C
(b)
120C
(c)
250C
(d)
200C
A rod of length 0.5m is heated at one end. On the steady state the temperatures at the ends of the rod are 100C
and 0C. The temperature at a point distance 10cm from the hot end will be
(a)
80C
(b)
60C
(c)
40C
(d)
20C
Four identical rods each of length l and of the same material are joined end-to-end to form a square. If the
temperature difference between the ends of a diagonal is 100C, then the temperature difference between the ends
of other diagonal will be
(a)
0C
(b)
100/lC
(c)
100/2lC
(d)
100C
A sphere, a cube and a thin circular plate made up of same material and having the same mass are initially heated
to a temperature of 200C. Which of these objects will cool slowest, when left in air at room temperature
(a)
sphere
(b)
cube
(c)
circular path
(d)
all will cool at the same rate
4
Q.12
Q.13
Q.14
Q.15
Q.16
Q.17
Q.18
Q.19
A body at 300C radiates 105J/m2. If sun radiates 109W/m2, then its temperature is
(a)
3000C
(b)
5457C
(c)
300  104C
(d)
5730C
A bucket full of water cools from 75C to 70C in time t1, from 70 to 65C in time t2 and from 65 in 65C in
time t3, then
(a)
t1 = t2 = t3
(b)
t1 > t2 > t3
(c)
t1 < t2 < t3
(d)
t1 > t2 < t3
If the emissive power and the absorptivity of a body at temperature T is E and A respectively, then the emissive
power of the black-body at temperature T will be
(a)
E/A
(b)
E/A.T
(c)
EA
(d)
EA/T
The ratio of wavelengths of emissive corresponding to the maximum emission in the spectrum of a black – body
heated to temperature 1000K and 2000K respectively is
(a)
¼
(b)
½
(c)
2
(d)
4
Two black – bodies A and B emit radiations with peak intensities at wavelengths 400nm and 800nm respectively.
If their temperatures are TA and TB respectively in kelvin scale and their emissive powers are EA and EB then
(a)
TA/TB = 2
(b)
EA/EB = 2
(c)
EA/EB = 8
(d)
EA/EB = 16
If the temperature of the sun becomes twice its present value, then radiated energy would be predominantly in the
(a)
ultraviolet region
(b)
X – rays region
(c)
Infra red region
(d)
Visible region
A solid sphere and a hollow sphere of the same material having equal radii are at the same temperature at the
instant t = 0
(a)
At t = 0, both will emit equal amount of energy per second
(b)
At t = 0, both will absorb equal amount of energy from the surroundings
(c)
At t = 0, the rate of cooling i.e., dT/dt will be the same
(d)
At t > 0, the two spheres will have lower but equal temperatures
Two bodies A and B have thermal emissivities 0f 0.01 and 0.81 respectively. The outer surface areas of the two
bodies are the same. The two bodies emit total radiation power at the same rate. The wavelength B corresponding
to maximum spectral radiancy in the radiation from B is shifted from the wavelength corresponding to maximum
spectral radiancy in the radiation from A, by 1.0m. If the temperature of A is 5802K.
(a)
The temperature of B is 1934K
(b)
B = 1.5m
(c)
The temperature of B is 11604K
(d)
The temperature of B is 2901K
Q.20
Heat is transferred most rapidly by the process of
Q.21
(a)
Conduction
(b)
Convection
(c)
Radiation
(d)
combustion
The high thermal conductivity of metal is due to free electrons. The relevant electron property :
Q.22
(a)
Its being charged
(b)
Convection
(c)
Radiation
(d)
Combustion
A metallic rod is continuously heated at its two ends, the flow of heat through the rod does not depend upon :
(a)
The area of cross-section of the rod
(b)
The mass of the rod
(c)
Q.23
Q.24
Time
(d)
The temperature gradient
The quantity of heat which crosses unit area of a metal plate during conduction depends upon :
(a)
The density of the metal
(b)
The temperature gradient perpendicular to the area
(c)
The temperature to which the metal is heated
(d)
The area of the metal plate
(b)
Thickness of the metal
The coefficient of thermal conductivity of a metal depends on :
(a)
Temperature difference between the two sides
5
(c)
Q.25
Q.28
Q.30
Q.31
Q.32
Q.33
Q.35
Q.36
Q.37
(b)
Js m-1K-1
(c)
Js m-1K
(d)
J s-1 m-1 K-1
K/T = constant
K/T = constant
(b)
(d)
K/ = constant
KL = constant
(a)
L = 50 cm, r = 1 cm
(b)
L = 100 cm, r = 2 cm
(c)
L = 25 cm, r = 0.5 cm
(d)
L = 75 cm, r = 1.5 cm
A 2 cm thick slab of commercial thermocole, 100 cm2 in cross-section and having thermal conductivity 2  10-4
cal sec-1 cm-1 (C)-1 has insulating regions differing by 100C. The quantity of heat flowing through it in a day
will be :
20.4 kcal
(b)
43.2 kcal
(c)
86.4 kcal
(d)
63.6 kcal
One end of copper rod of length 1.0 m and area of cross-section 10-3 m2 is immersed in boiling water and the other
end in ice. If the coefficient of thermal conductivity of copper is 92 cal/m s C and the latent heat of ice is 8  10-4
cal/kg, then the amount of the ice which will melt in one minute is :
(a)
9.2  10-3 kg
(b)
8  103 kg
(c)
6.9  10-3 kg
(d)
5.4  10-3 kg
Four identical copper cylinders are painted; if they are all heated to the same temperature and left in vacuum,
which will cool most rapidly.
(a)
Painted shiny white
(b)
Painted rough black
(c)
Painted shiny black
(d)
Painted rough white
A polished metal with rough black spot on it is heated to about 1400 K and quickly taken to a dark room. Which
one of the following statements will be true?
(a)
The spot will appear brighter than the plate
(b)
The spot will appear darker than the plate
(c)
The spot and plate will be equally bright
(d)
The spot and plate will not be visible in dark
A piece of red glass when heated in dark to red hot state will appear to be :
(a)
White
(b)
Red
(c)
Green
(d)
Invisible
Fraunhofer lines in the spectrum of sun are explained by :
(a)
Q.34
Js-1mK-1
Two end of rods of length L and radius r of the same material are kept at the same temperature. Which of the
following rods conducts most heat :
(a)
Q.29
None of the above
If K and  respectively are the thermal and electrical conductivities of a metal at a absolute temperature T, then :
(a)
(c)
Q.27
(d)
The S.I. unit of thermal conductivity is :
(a)
Q.26
Area of the plate
Wien’s law
(b)
Planck’s law
(c)
Newton’s law (d)
Kirchhoff’s law
The total radiation emitted by a perfectly black body is proportional to :
(a)
Temperature on ideal gas scale
(b)
Fourth root of temperature on ideal gas scale
(c)
Fourth power of temperature on ideal gas scale
(d)
Square of temperature on ideal gas scale
If the temperature of the sun is doubled, the rate of energy received on earth will be increased by a factor of :
(a)
2
(b)
4
(c)
8
(d)
16
A black body at a high temperature T K radiates energy at the rate E watt/m2; when the temperature falls to (T/2)
K the radiated energy will be :
(a)
E/4
(b)
E/2
(c)
2E
(d)
E/16
The temperature of a body is increased from 27C to 127C. The radiation emitted by it increase by a factor of :
6
(a)
Q.38
Q.39
Q.40
Q.41
Q.42
Q.45
Q.46
Q.47
Q.48
Q.49
Q.50
Q.51
(15/9)
(c)
(4/3)
(d)
(12/27)
As the temperature of a black body increases, the wavelength of the emitted radiation of maximum intensity
(a)
Increases
(b)
Decreases
Remains unchanged
According to Wien’s displacement law :
(a)
Increases
(c)
Q.44
(b)
According to Newton’s law of cooling (provided the difference of temperature is small) the rate of loss of heat is
proportional to :
(a)
The excess temperature
(b)
The square of the excess temperature
(b)
The cube of the excess temperature
(d)
The fourth power of the excess temperature
A body in a room cools from 90C to 80C in 5 minute. The time taken to cool from 70C to 60C is :
(a)
5 minute
(b)
Less than 5 minute
(c)
More than 5 minute
(d)
Less or more than 5 minute depending on the nature of the liquid.
In a room where the temperature is 30C a body cools from 61C to 59C in 4 minute. The time taken by the body
to cool from 51C to 49C will be :
(a)
4 minute
(b)
6 minute
(c)
5 minute
(d)
8 minute
A pan filled with hot food cools from 500C to 49.9 C in 5 sec. How long will it take to cool from 40.0 C to
39.9C if the room temperature is 30C?
(a)
2.5 s
(b)
10 s
(c)
20 s
(d)
5s
(c)
Q.43
(256/81)
Remains unchanged
(d)
Depends on the material of the black body
(b)
Decreases
(d)
Depends on the material of the black body
The intensity of radiation emitted by the sun has its maximum value at a wavelength of 510 nm and that emitted
by the North Star has the maximum value at 350 nm. If these stars behave like black bodies, th4en the ratio of the
these stars bodies, then the ratio of the surface temperature of the Sun and the North Star is :
(a)
1.46
(b)
0.69
(c)
1.21
(d)
0.83
A black body is at a temperature of 2800K. The energy of radiation emitted by this object with wavelength
between 499nm and 500nm is U1, between 999 nm and 1000nm is U2 and between 1499nm and 1500nm is U3.
The Wein’s constant, b =2.88 x 106nm –K. Then:
(a)
U1 =0
(b)
U3 =0
(c)
U1 >U2
(d)
U2 >U1
A spherical black body with a radius of 12cm radiates 450W power at 500K. if the radius were halved and the
temperature doubled, the power radiated in watt would be
(a)
225
(b)
450
(c)
900
(d)
1800
A black body at a temperature of 1640 K has the wavelength corresponding to maximum emission equal to
1.75 . Assuming the moon to be a perfectly black body, the temperature of the moon, if the wavelength
corresponding to maximum emission is 14.35 is :
(a)
100K
(b)
150 K
(c)
200
(d)
250
According to Newton’s law of cooling, the rated cooling of a body is proportional to ()n, when  is the
difference of the temperature of the body and the surroundings and n is equal to
(a)
Two
(b)
three
(c)
four
(d)
one
In the Ingen Hauze’s experiment the was melts upto length 10 and 25 cm on two identical rods of different
materials. The ratio of thermal conductivities of the two materials is :
(a)
1 : 6.25
(b)
625 : 1
(c)
1 : 2.5
(d)
1 : 2.5
A black body is at a temperature 300 K. It emits energy at a rate, which is proportional to :
(a)
300
(b)
(300)3
(c)
(300)2
(d)
(300)4
Two spheres of the same material have radii 1m and 4m and temperature 4000K and 2000 K respectively. The
ratio of the energy radiated per second by the first sphere to that by the second is :
(a)
1:1
(b)
16 : 1
(c)
4:1
(d)
1:9
7
Q.52
Q.53
Q.54
Infrared radiation is detected by :
(a)
spectrometer (b)
pyrometer
(c)
nanometer
(d)
photometer
A hot and a cold body are kept in vacuum separated from each other. Which of the following will cause decrease
in temperature of the hot body?
(a)
Radiation
(b)
Convection
(c)
Conduction
(d)
Temperature remains unchanged
A black body at 1227C emits radiation with maximum intensity at a wavelength of 5000Å. If the temperature of
the body is increased by 1000C, the maximum intensity will be observed at :
(a)
4000 Å
(b)
5000 Å
(c)
6000 Å
(d)
3000 Å
ANSWER SHEET
1.
(c)
2.
(b)
3.
(d)
4.
(b)
5.
(b)
6.
(c)
7.
(a)
8.
(c)
9.
(a)
10.
(a)
11.
(a)
12.
(b)
13.
(c)
14.
(a)
15.
(c)
16.
(a),
(d)
17.
(a)
18.
(a),
(b)
19.
(a), (b)
20.
(c)
21.
(c)
22.
(b)
23.
(b)
24.
(d)
25.
(d)
26.
(a)
27.
(b)
(c)
29.
(c)
30.
(b)
31.
(a)
32.
(d)
33.
(d)
34.
(c)
35.
(d)
36.
(d)
37.
(a)
38.
(a)
39.
(a)
40.
(b)
41.
(b)
42.
(b)
43.
(b)
44.
(b)
45.
(d)
46.
(d)
47.
(c)
48.
(d)
49.
(a)
50.
(d)
51.
(a)
52.
(b)
53.
(a)
54.
(d)
28.
8
9
WAVES OBJECTIVE QUESTION
Q.1
Q.2
Q.3
Q.4
Q.5
Q.6
Q.7
Q.8
Q.9
Q.10
A transverse wave is described by y= y0sin 2 (ft - x), the maximum particle velocity is equal to four times the
wave velocity if.
(a)
 = y0/4
(b)
 = y0/2
(c)
 = y0
(d)
 = 2y0
-4
A wave equation which gives the displacement along the y-direction is given by y = 10 sin (60t +2x), where x
and y are in metres and t is in seconds. This represents a wave
(a)
traveling with a velocity of 30 m/s in the negative x-direction
(b)
of wavelength  meters
(c)
of frequency 30/ hertz
(d)
of amplitude 104 metre traveling along the negative x-direction
A wave is represented by the equation
Y = A sin (10 x + 15 t + /3)
where is in metres and t is in seconds. The expression represents
(a)
a wave traveling in the positive x-direction with a velocity 1.5 m/s
(b)
a wave traveling in the negative x-direction with a velocity 1.5 m/s
(c)
a wave traveling in the negative x-direction having a wavelength 0.2 m
(d)
a wave traveling in the positive x-direction having a wavelength 0.2 m
Which of the following equations does not represent a progressive wave ?
(a)
y = A sin k (x + t)
(b)
y =  (x - t)
(c)
y = a log (x - t)
(d)
y =  (x2 - 2t3)
The displacement of a particle in a string stretched in x-direction is represented by y. Among the following
expressions for y, those describing wave motions are
(a)
cos k x sin t
(b)
k2 x2 - 2 t2
(c)
cos2 (kx + t)
(d)
cos (k2 x2 - 2 t2)
A bumb with the equation y = 2  10-3 e(x-4t)2 is traveling on a string 1m long, where distances are in metres and
time in seconds. If the tension in the string is 16 N, the mass of the string is
(a)
1.6 g
(b)
4.0 g
(c)
10 g
(d)
16 g
Out of the following, the equation for a cylindrical progressive wave is
(a)
y = A sin t
(b)
y = a/x sin (t – kx)
(c)
y = A sin (t - kx)
(d)
y = a/x sin (t – kx)
Of the following the equation of a spherical progressive wave is
(a)
y = A sin t
(b)
y = A sin (t – kr)
(c)
y = A/r sin (t - kr)
(d)
y = A/r sin (t – kr)
A sound wave has frequency of 550 Hz, velocity of 330 m/s and amplitude of 0.1 mm.
(a)
The distance between two points having a phase difference of 60 is 0.1 m.
(b)
The phase difference between two points separated by a distance of 0.3 m is /2.
(c)
The maximum particle velocity is 0.11  m/s.
(d)
The minimum particle velocity is zero.
A sinusoidal wave is traveling in a medium. Then
(a)
the minimum distance between two particles having the same speed is /2
(b)
the minimum distance between two particles in the same phase is .
(c)
the phase difference between two particles separated by a distance of 5/4 along the direction of
propagation of wave is /4.
(d)
If its equation is 0.02 sin (5t – 0.2 x), the maximum particle velocity is 0.1 m/s.
Aurora Classes
10
Waves
Q.11
Q.12
Q.13
Q.14
Q.15
Q.16
Q.17
Q.18
Q.19
Q.20
Q.21
Q.22
Q.23
Two waves are represented by
y1 = sin 5 sin 2 (75 t – 0.25 x)
y2 = 10 sin 2 (150 t – 0.50 x)
The intensity ration I1/I2 of the two waves is
(a)
1:2
(b)
1:4
(c)
1:8
(d)
1 : 16
An intensity level of zero decibel corresponds to sound wave of intensity in W/m2 to
(a)
zero
(b)
10
(c)
10-12
(d)
10-16
In an observer moves twice the distance away from a point source of sound, the intensity level falls by
(a)
2 dB
(b)
3 dB
(c)
4 dB
(d)
6 dB
If we turn off one of the speakers of a stereo system, the intensity change in dB is
(a)
0.5
(b)
2.0
(c)
3
(d)
4
2
Sound waves whose intensities exceed 1 W/m cause damage to human ears. This corresponds in dB to
(a)
1
(b)
1.2
(c)
12
(d)
120
If two waves of the same frequency and same amplitude superpose and produce a disturbance having the same
amplitude as that of any one of the component waves, the two waves differ in the phase by
(a)

(b)
2/3
(c)
/2
(d)
0
Due to arrival of four waves, a particle has following displacements simultaneously at a certain instant
y1 = 5 sin 314 t
y3 = 5 sin (314 t - )
y2 = 5 sin (314t -2)
y4 = 5 sin (314t -3/2)
The amplitude of the resultant wave is
(a)
0
(b)
5
(c)
52
(d)
10
If the ratio of maximum to minimum intensity in an interference pattern is 49 : 1 then, the ration between
amplitudes of two interfering waves is
(a)
6:1
(b)
37 : 35
(c)
1:6
(d)
4:3
Two waves of intensities I and 4 I produce interference. The intensity constructive and destructive interference
respectively is
(a)
3 I, 5 I
(b)
5I, 3 I
(c)
I, 9 I
(d)
9 I, I
Two waves of the same frequency produce interference. They have amplitudes in the ratio of 1 : 3. The intensity
of the first wave is I, then
(a)
the intensity at the constructive interference is 16 I
(b)
the intensity at the destructive interference is 4 I
(c)
the intensity at the destructive interference is zero
(d)
the ratio of Imax / Imin is 4
Beats are produced die to superposition of two vibrations
y1 = 4 sin 400 t
y2 = 3 sin 404 t
situated very near to the ears of a person. The person hears
(a)
2 beats/second with intensity ratio 4/3 between maxima and minima
(b)
2 beats/second with intensity ratio 49/1 between maxima and minima
(c)
4 beats/second with intensity ratio 7/2 between maxima and minima
(d)
4 beats/second with intensity ratio 4/3 between maxima and minima
50 tuning forks are so arranged in series that each fork give 5 beats per second with the previous one. If the last
fork gives the octave of the first, the frequency of the later is
(a)
245 Hz
(b)
250 Hz
(c)
240 Hz
(d)
260 Hz
A tuning fork of frequency 90 Hz is sounded and moved towards an observer with a velocity equal to one-tenth
the velocity of sound. The note heard by the observer will have a frequency in Hz
Aurora Classes
11
Waves
Q.24
Q.25
Q.26
Q.27
Q.28
Q.29
Q.30
Q.31
Q.32
Q.33
Q.34
Q.35
(a)
100
(b)
90
(c)
80
(d)
95
An engine is moving on a circular path of radius 100 m with a speed of 20 m/s. What will be the frequency
observed by an observer standing stationary at the center of the circular path when the engine blows whistle of
frequency 500 Hz. (Speed of sound 340 m/s)
(a)
510 Hz
(b)
500 Hz
(c)
490 Hz
(d)
480 Hz
If the frequency of a note emitted by a source changes by 20% as it approaches an observer. As it recedes away
from him, the apparent frequency
(a)
20%
(b)
17.4 %
(c)
16.67 %
(d)
14.3 %
The wavelength of light received from a galaxy is 4% greater than that received from an identical source of the
earth. The velocity of the galaxy relative to the earth is
(a)
7  106 m/s
(b)
12  106 m/s
(c)
0.75  106 m/s
(d)
1.33  106 m/s
A sharp tap is made by an observer standing in front of stairs, the width of whose tread is 25.0 cm. If the velocity
of sound is 330 m/s the frequency of the note heard by him in Hz is
(a)
1320
(b)
660
(c)
445
(d)
990
The equation of a stationary wave on a stretched wire is
Y= 8sin x/45 sin 30t.
Where all distance are in cm and time in seconds
(a)
The distance between two nodes is 45cm.
(b)
The maximum amplitude of vibration is 8cm.
(c)
Two particle on the two sides of a note vibrate with a phase difference of /2.
(d)
All particles vibrate with the same frequency of 15Hz.
A wave represented by the equation y = a cos (km-t) is superposed with another wave to from stationary wave
such that the point x = 0 is node. The equation for the other wave is
(a)
a sin (kx+t)
(b)
-a cos (kx-t)
(c)
-a cos (kx+t)
(d)
cos (k2 x2 + 2 t2)
The displacement of a particles in a string in the x-direction is represented by y. Among the following expression
for y, those describing wave motion are.
(a)
cos kx sint
(b)
cos2(kx + t)
(c)
k2x2- 2t2
(d)
cos (k2x2- 2t2)
A wave described by y = A cos (t- kt +) is totally reflected from a fixed end. After reflection which may
change,
(a)

(b)

(c)
 and  (d)
k
The displacement y of a particle executing periodic motion is given by
Y=4 cos2 [½t] sin (1000t)
This expression may be considered to be a result of the superposition of
(a)
two
(b)
three
(c)
four
(d)
five
A stretched string of length L fixed at its ends can sustain stationary waves of wavelength  given by
(a)
=2L
(b)
 = 2L/n
(c)
 = L/n
(d)
 = Ln2
The vibrations of a stretched string fixed at both ends are described by y = 4sin 2x cos t. The minimum length
of the wire will be
(a)
1m
(b)
0.5m
(c)
5m
(d)
2m
Two identical straight wires are stretched so as to produce 6 beats per second when vibrating Simultaneously. On
changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by T1, T2 the higher
and the lower initial tensions in he strings, then it could be said that while making the above changes in tension.
(a)
T2 was decreased
(b)
T2 was increased
(c)
T1 was increased
(d)
T1 was decreased
Aurora Classes
12
Waves
Q.36
Q.37
Q.38
Q.39
Q.40
Q.41
Q.42
Q.43
Q.44
Q.45
An air column in a pipe, which is closed at one end, will be in resonance with a tuning fork of frequency 264Hz if
the length of the column (in cm) is
(a)
31.25
(b)
62.50
(c)
93.75
(d)
125
A tube, closed at one end and containing air, produces, when excited, the fundamental note of frequency 512Hz.
If the tube is open at both ends the fundamental frequency that can be excited is
(a)
1024Hz (b)
512Hz
(c)
256Hz
(d)
128Hz
An organ pipe P1 closed at one end vibrating with its first harmonic and another pipe P2 open at both ends
vibrating in its third harmonic are in resonance with a giving tuning fork. The ratio of the length of P1 to P2 is
(a)
8/3
(b)
3/8
(c)
½
(d)
1/6
Velocity of sound in air is 320 m/s. A pipe closed at one end has length 1m. Neglecting end corrections, the air
column in the pipe can resonate for sound of frequency:
(a)
80Hz
(b)
240Hz
(c)
320Hz
(d)
400Hz
An air column closed at one end is vibrating in its fifth harmonic. If the frequency of this harmonic wave were n
times the fundamental note emitted by air in the same tube when opened at both ends, n would be equal to
(a)
2.5
(b)
3.0
(c)
4.5
(d)
5.0
A cylindrical tube, open at both ends has as fundamental frequency f in air. The tube is dipped vertically in water
so that half of it is in water. The fundamental frequency of air column is now
(a)
f/2
(b)
3f/4
(c)
f
(d)
2f
The end correction of a resonance column is 1.0cm. If the shortest length resonating with a tuning fork is 15.0 cm,
the next resonating length is
(a)
31cm
(b)
45cm
(c)
46cm
(d)
47cm
A closed organ pipe and an open organ pipe have their first overtones identical in frequency, their lengths are in
the ratio
(a)
1:2
(b)
2:3
(c)
3:4
(d)
4:5
In a certain organ pipe three successive resonance frequencies ate at 425, 595 and 765 Hz. If the speed of sound in
air is 340m/s, the length of the pipe is
(a)
2m
(b)
1m
(c)
1.5m
(d)
2.m
A tuning fork and a sonometer wire emitting its fundamental note gives 5 beats per seconds both when the length
of the wire is 1m or 1.05m. The velocity of transverse wave in the sonometer wire is
(a)
420 m/s (b)
400m/s
(c)
210m/s
(d)
200m/s
Aurora Classes
13
Waves
ANSWER SHEET
1.
(b)
2.
(a),(b), (c), (d)
3.
(b), (c)
4.
(c), (d)
5.
(a), (c)
6.
(c)
7.
(b)
8.
(c)
9.
(a), (c), (d)
10.
(a), (b), (d)
11.
(d)
12.
(c)
13.
(d)
14.
(c)
15.
(d)
16.
(b)
17.
(c)
18.
(d)
19.
(d)
20.
(a), (b), (d)
21.
(b)
22.
(a)
23.
(a)
24
(b)
25.
(d)
26.
(b)
27.
(b)
28.
(a), (b), (d)
29.
(c)
30.
(a), (b)
31.
(a)
32.
(b)
33.
(b)
34.
(b)
35.
(b), (d)
36.
(a), (c)
37.
(a)
38.
(d)
39.
(a), (b), (d)
40.
(a)
41.
(c)
42.
(d)
43.
(c)
44.
(b)
45.
(c)
Aurora Classes
14
Waves