Download Class XI-Physics 2016-17

Kendriya Vidyalaya AFS Manauri Allahabad
CUMULATIVE (HALF YEARLY) EXAMINATION 2016-2017
Subject - Physics (Theory)
Time: – 3 hrs.
Class: – XIth
M.M.: – 70
Blue Print
S.No. Name of the Unit
VSA
SA I
SA II
LA
LA
Total
1mark 2marks 3 marks 4 marks 5 marks
01
Physical World and measurement
2 (1)
----
3 (1)
-----
-----
5
02
Kinematics
-----
2 (1)
3 (2)
-----
5 (1)
13
03
Laws of motion
----
2 (1)
3 (2)
5(1)
13
04
Work , Power and Energy
1(1)
2 (1)
3 (2)
-----
-----
9
05
Motion of systems of particle and rigid ----bodies
2 (1)
3 (1)
4(1)
-----
9
06
Gravitation
1(1)
------
3 (3)
-----
-----
10
07
Properties of bulk matter
1(1)
2 (1)
3 (1)
-----
5 (1)
11
Total
1x5 = 2x5 = 3x12 = 4x1=4
5
10
36
5x3
15
= T.Q.=
26
T.M.=
70
Kendriya Vidyalaya AFS Manauri Allahabad
CUMULATIVE (HALF YEARLY) EXAMINATION 2016-2017
Subject - Physics (Theory)
Time: – 3 hrs.
Class: – XIth
M.M.: – 70
a) All questions are compulsory.
b) There are 26 questions in all. Questions from 1 to 5 carry 1 mark each, questions from 6
to 10 carry two marks each, questions from 11 to 22 carry three marks each, question 23
carries 4 marks and questions from 24 to 26 carry five marks each.
c) There is no overall choice. However an internal choice has been provided in one question
of two marks, one question of three marks and in all three questions of 5 marks. You
have to attempt only one of the choices in such questions.
d) Use of calculators is not permitted.
1.
2.
3.
4.
5.
Name the forces having the longest and shortest range of operation.
When momentum of a body is doubled, how will its kinetic energy change?
What is meant by a geostationary satellite?
When does the streamline flow become turbulent?
Find the dimensions of a and b in the equation E = (b-x2)/at where E is energy, x is
distance, t is time?
6. The position time(x-t) graphs per two children A and B
returning from there school O to their homes P and Q
respectively are shown in figure.
(a) Who lives closer to the school?
(b) Who started from school earlier?
(c) Who walks faster?
(d) Who will overtake the other on the road?
7. Derive Newton’s third law of motion from Second law of motion.
8. Prove work energy theorem for variable force?
9. Calculate the moment of inertia of a cylinder of length L= 150cm, radius R= 5cm,
density= 8 gcm-3 about the axis of cylinder?
10. (a) Assuming the earth to be of uniform density; how much would a boy weigh half way
down to the center of the earth if he weighed 450 N on the surface?
11. A hydraulic automobile left is designed to left cars with a maximum mass of 3000 kg.
The area of cross section of the piston carrying the load is 425 cm2. What maximum
pressure would the smaller piston have to bear?
OR
During blood transfusion the needle is inserted in a vein where the gauge pressure is 2000
Pa. At what height must the blood container be placed so that blood may just enter the
vein? The density of whole blood = 1.06 x 103 kg m-3.
12. (a) The percentage errors in the measurement of mass and speed are 2% and 3%
respectively. What will be the maximum %error in the estimation of kinetic energy?
(b) What will be the least count of a vernier caliper with 20 divisions on the sliding scale?
13. Two trains A and B, each of length 100 m are running on parallel tracks, one overtakes
the other in 20 sec and one cross the other in 10 sec. calculate the velocities of each train.
14. (a) State parallelogram law of vector addition of two vectors.
(b) Find the magnitude and direction of the resultant of two vectors if they are acting
along mutually opposite directions.
(c) Find the vector AB and its magnitude if it has initial point A (1, 2, -1) and final point
B (3, 2, 2).
15. A spring weighing machine hanging in the side of a stationary lift reads 50 Kg, when a
man stands on it. What would happen to the scale reading if the lift is moving
(i)
Upward with constant velocity.
(ii)
Upward with constant acceleration 1.2 ms-2.
(iii)
Downward with constant acceleration 1.2 ms-2.
16. (a) Why does an athlete run some steps before taking a jump?
(b) Why does a cricket player lower his hands while catching a ball?
17. Define conservative force. Show that the total mechanical energy of a freely falling body
remains constant throughout its fall.
18. A railway carriage of mass 9000 kg moving with a speed of 36 kmh-1 collides with a
stationary carriage of the same mass. After the collision, the carriages get coupled and
move together. What is there common speed after collision? What type of collision is
this?
19. (a) Derive the relation between torque and angular momentum.
(b) Find the torque of a force 7i - 3ĵ - 5k about the origin which acts on a particle whose
position vector is i + ĵ - k. Where i, ĵ and k represent unit vector along x, y and z
direction respectively.
20. (i) State kepler’s law of (a) orbits and (b) areas.
(ii)The time period of the satellite of the earth is 5 hours. If the separation between the
earth and the satellite is increased to 4 times the previous value, then what will be the
new time period of the satellite?
21. Define escape velocity. Derive a relation for escape velocity from the surface of the earth.
Write its value also.
OR
Define orbital velocity of a satellite. Derive expressions for the orbital velocity of a
satellite. Show that the escape velocity of a body from the earth’s surface is √2 times its
velocity in a circular orbit just above the earth’s surface.
22. (a) Derive an expression for the excess pressure inside a liquid drop.
(b)Why excess pressure in a soap bubble is twice the excess pressure of a liquid drop of
the same radius?
23. (a) A person is standing on a rotating table with metal spheres in his hands. If he
withdraws his hands to his chest, what will be the effect on his angular velocity? Justify?
(b) Find the expression for the velocity of a body rolling down on the inclined plane
without slipping.
24. Define projectile. Show that the path of projectile is parabola. Obtain expression for the
horizontal range. At what value of θ is the horizontal range maximum ? Find maximum
horizontal range also.
OR
Define uniform circular motion. Derive relation for centripetal acceleration and its
direction. Draw related diagrams. A stone tied to 14 m string is whirled in a horizontal
circle at the rate of 10 revolutions in 5 seconds. Find its angular velocity and linear
velocity.
25. (a) Derive an expression for the safe limit of velocity of a vehicle negotiating a turn on
the banked road with the help of labeled diagram showing all the forces acting on the
vehicle.
(b) A circular race track of radius 300 m is banked at an angle of 150. If the coefficient of
friction between the wheels of a race car and the road is 0.2. What is the maximum speed
of the race car to avoid wear and tear on its tyres?
OR
(a) Derive an relation between angle of friction and angle of repose.
(b) A mass of 200 kg is resting on a rough inclined plane of 30 o. If the coefficient of
friction is 1/√3, find the least and the greatest forces acting parallel to the plane to
keep the mass in equilibirium.
26. State and prove Bernoulli’s theorem. Explain the working of venturimeter with proper
expressions.
OR
Describe different modes of heat transfer. A copper block of mass 2.5 kg is heated in a
furnace to a temperature of 5000 C and then placed on a large ice block. What is the
maximum amount of ice that can melt? (Specific heat of copper =0.39 J g-1K-1& heat of
fusion of water =335 J g-1)
Marking Scheme
Kendriya Vidyalaya AFS Manauri Allahabad
CUMULATIVE (HALF YEARLY) EXAMINATION 2016-2017
Subject - Physics (Theory)
1. longest range force is gravitational force and nuclear force is shortest range force.
1M
2
2. K.E.=p /2m ,K.E. becomes 4 times.
1M
3. A satellite which revolves around the earth in its equatorial plane with the same angular speed
and the same direction as the earth rotates about its own axis is called a geostationary satellite.
1M
4.
5.
6.
7.
8.
9.
When the velocity of liquid exceeds critical velocity.
a = M-1T, b = L2
(a) A, (b) A, (c) B, (d) B
For correct derivation.
For correct derivation.
Mass of cylinder = volume X density = 30000 π g
Moment of inertia I = MR2/2= 1.2X106 gcm2
10. (a) w=mg=450N, d=R/2
g’=g(1-d/R)
w’=w(1-d/R)
w’=450(1-R/2/R)=450/2
w’=225N
11. Pressure on larger piston ,P = mg / A
1M
(½+½)M
For each part, half(1/2) Marks
2M
2M
1M
1M
(1 )M
( ½ )M
(1)M
( ½ )M
½M
= 6.92 x 105 N m-2
½M
A/C to Pascal’s law , pressure transmitted on smaller piston = 6.92 x 105 N m-2
OR,
Height of the container , h = Pg / ρg = 0.1925 m
12. (a) For correct formula ,
½ Marks ,
1M
(1+1) M
% error in K.E. = 2% + 2 x 3% =8% ,
(b) L.C = 1 MSD – 19/20 MSD = 1x1mm / 20 = 0.005 cm
½M
1 M
13. Let u and v be the velocities of trains A and B respectively.
During overtaking , R.V. of A w.r.t.B = u – v
½M
During crossing , R.V. of A w.r.t.B = u + v
½M
Total distance to be covered by A during overtaking or crossing = 100 + 100 = 200 m
200
𝑢−𝑣
= 20
and
200
𝑢+𝑣
= 10
u- v = 10 and u + v = 20
( ½+½)M
on solving , u =15 ms-1 , v = 5 ms-1
(½+½)M
14. (a) correct statement
1M
(b)R = +ve difference between two vectors acts along the bigger vector.
1M
(c) Vector AB = 2i +3j , Where i & j are unit vectors
1M
15. (i) w = mg = 50 kgf
1M
(ii) w = m (g + a) = 50x 11 N = 56.12 kgf
1M
(iii)w = m (g - a) = 50x 8.6 N = 43.88 kgf
1M
16. (a) To provide necessary centripetal force caused by horizontal component of normal
reaction of the ground.
1M
(b) Inertia of motion help him to take longer jump.
1M
(c) To increase time duration for the reduction of force on the hand.
1M
17.
(Correct definition + figure + proof )
(½+½+2)M
18. By conservation of momentum , m1u1 + m2u2 = ( m1 + m2 ) v
On solving ,
½M
v = 5 ms-1
½M
Total K.E. before collision = 450000 J, Total K.E. after collision = 22500 J,
(½+½)M
Total K.E. after collision < Total K.E. before collision , inelastic collision ,
(½+½)M
19. (a) For derivation of correct relation, vector ι =
𝑑𝐿
1½M
𝑑𝑡
(b). vector ι = vector r x vector F = - 8i – 2j – 10 k
1½M
20. (i) Correct statement of laws of (orbits + areas )
(ii) (
𝑇2
5
4 𝑅1 2
) , or
𝑅1
)2 =(
( 1 + 1) M
T2 = √64 𝑋 25 = 40 h
1M
21. Definition + Derivation + Value
( ½ +2+½)M
OR , Definition + Derivation + Proof
22. (a) Derivation ,
2 ½ Marks
( ½ + 1 ½ + 1) M
(b) Due to two free surface ,
½M
23. (a) Moment of inertia decreases , A/C to conservation of angular momentum,
angular velocity increases.
2𝑔ℎ
(c) For proof , v = √1+𝑘2/𝑅2 , 1M ,
10𝑔ℎ
V sphere = √
7
, ½M,
1M
v ring = √𝑔ℎ ,
½M ,
4𝑔ℎ
v cylinder =√
3
Sphere will reach with maximum velocity ,
,½M
½M
24. Definition + Diagram + Expression showing parabolic path
2
For proof of horizontal range , R = (u sin2)/g
 = 450
Rmax. = u2/g
(½+½+1½)M
1M
½M
1M
OR
Definition + Derivation + Direction +Diagram
=
10
5
(½ + 2 + ½ + ½) M
= 2 rev./sec.
 = 2 = 4 rad./sec.-1
Linear velocity = r = 14x4 = 176 ms -1
25. (i) Correct labeled diagram + proof
(ii) vo = √rg tan 𝜃 = 28.1 ms -1
OR
(i) Correct labeled diagram + proof
½M
½M
½M
(1 + 2 ½ ) M
1½M
(½ +2 )M
(ii) Figure + force of friction = μ mg cos θ = 980 N
(½+½)M
Component of the weight acting down the inclined plane
= mg sin θ =980 N
½M
Least force = mg sin θ – f = 980 - 980 = 0
½M
Greatest force = mg sin θ + f = 980 + 980 = 1960 N
½M
26. Statement + Labeled diagram + Derivation
(1+½ +2½)M
If the surface tension of oil is less than that of water, then it spreads on
water. If the surface tension of oil is more than that of water, then it
floats as drops on water.
1M
OR
Three modes with there properties
M’=msΔt/L; M’=1455g=1.5 kg
(1+1 +1) M
2M