Download waves in elastic medium and acoustics

Coulomb’s Law
Objective Question
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
Q.15
Q.16
Q.17
When a glass rod is rubbed with silk, it acquires a positive charge because:
(a)
protons are added to it
(b)
electrons are added to it
(c)
electrons are removed to it
(d)
protons are removed from it.
The number of electrons contained in 1 coulomb of charge equals :
(a)
6.25  1017
(b)
6.25  1018
(c)
6.25  1019
(d)
1.6  1019
Two charges +1 C and + 5 C are placed a distance apart. The ratio of the forces acting on them are :
(a)
1:5
(b)
5:1
(c)
1 :1
(d)
1 : 25
The ratio of the forces between two tiny bodies with constant charges in air and an insulating medium of
dielectric constant K is :
(a)
1:K
(b)
K:1
(c)
1 : K2
(d)
K2 : 1
The dielectric constant K of an insulater can be :
(a)
-1
(b)
0
(c)
0.5
(d)
5.
The SI unit of free-space permittivity 0 is :
(a)
Nm2C-2
(b)
Nm-2C2
(c)
N-1m-2C2
(d)
N-1m2C2.
The ratio of the gravitational and the electrostatic forces between two electrons at some distance apart is :
(a)
1043
(b)
1039
(c)
10-39
(d)
10-43.
Three charges 4q, Q and q are in a straight line in the position 0, l/2 and re and l respectively. Resultant force
at q will be zero if Q is equal to :
(a)
-q
(b)
-2q
(c)
-q/2
(d)
4q.
A charge q is placed at the center of the line joining two equal charges Q. The system of the three charges will
be in equilibrium if q is equal to :
(a)
-Q/2
(b)
-Q/4
(c)
+Q/4
(d)
Q/2.
Two point charges + 4C and + 2C repel each-other with a force of 8N. If a charge of -4C is added to each
of these charges, the force would be
(a)
zero
(b)
8N
(c)
4N
(d)
12N
Two point charges certain distance apart in air repel each other with a force F. A glass plate is introduced
between the charges. The force becomes F`, where
(a)
F` < F
(b)
F` = F
(c)
F` > F (d)
data is insufficient.
Force between two charges separated by a certain distance in air is F. If each charge were doubled and
distance between them also doubled, force would be
(a)
F
(b)
2F
(c)
4F
(d)
F/4
When a body is charged by induction, then the body
(a)
becomes neutral
(b)
does not lose any charge
(c)
loses whole of the charges on it
(d)
loses part of the charge on it
A polythene piece, rubbed with wool, is found to have negative charge of 4  10-7C. The no. of electrons
transferred from wool to polythene are
(a)
1.5  1012
(b)
2.5  1012
(c)
2.5  1013
(d)
3.5  1013
-7
When a piece of polythene is rubbed with wool, a charge of –2  10 C is developed on polythene. What is
the amount of mass, which is transferred to polythene?
(a)
5.69  10-19 kg
(b)
6.25  10-19 kg
-19
(c)
9.63  10 kg
(d)
11.38  10-19 kg
If a body is positively charged, then it has
(a)
excess of electrons
(b)
excess of protons
(c)
deficiency of electrons
(d)
deficiency of neutrons
On charging by conduction, mass of a body may
(a)
increase
(b)
decrease
(c)
(d)
none.
increase or decrease
1
Q.18
Q.19
An uncharged insulted conductor A is brought near a charged insulted conductor B.
(a)
(b)
the charge and potential of B, both remain constant
both change
(c)
the charge remains constant, but potential decreases
(d)
the charge remains constant but potential increases
A given charge is situated at a certain distance from an electric dipole in the end on position, experiences, a
force F. If the distance of charge is double, the force acting on the charge will be
(a)
Q.20
F
(b)
F/2
(c)
F/4
(d)
F/8
Point charges +4q, -q and +4q are kept on the x-axis at points x = 0, x = a and x = 2 a respectively
(a)
only -q is in stable equilibrium
(b)
all the charges are in stable equilibrium
(b)
all the charges are in unstable equilibrium
(d)
none of the charges in equilibrium
Q.21 There are two charges +1C and +5C. The ratio of the force the acting on them will be
(a)
1:1
(b)
1:2
(c)
1:3
(d)
1:4
Q.22
Q.23
Q.24
Q.25
Q.26
Q.27
Q.28
Q.29
Q.30
Coulomb’s law is true for
(a)
atomic distances (= 10-11 m)
(b)
nuclear distance (= 10-15 m)
(c)
charged as well as for uncharged particles
(d)
all the distances
Two charges are placed a certain distance apart. A metallic sheet is placed between them. What will happen to
the force between the charges?
(a)
increase
(b)
decrease
(c)
remain unchanged
(d)
either ‘a’ or ‘b’.
Two equally charged identical metal spheres A and B repel each other with a force 3  10-5 N. Another
identical uncharged sphere C is touched to A and then placed at the mid-point between A and B. Net force on
it is
(a)
1  10-5N
(b)
2  10-5N
(c)
1.5  10-5N
(d)
3  10-5N
Which of the following is best insulator ?
(a)
Carbon
(b)
Paper
(c)
Graphite
(d)
Ebonite.
A cylindrical conductor is placed near another positively charged conductor. The net charge acquired by the
cylindrical conductor will be
(a)
positively only
(b)
negative only
(c)
zero
(d)
either positive or negative.
The point charges of 10C and –5 C are separated in air by 1m. The ratio of force exerted by one on the
other is
(a)
1:2
(b)
2:1
(c)
1:1
(d)
none of the above.
An attractive force of 5 N is acting between two charges of + 2C and - 2C placed at some distance. If the
charges are mutually touched and placed again at the same distance, the new force would be
(a)
4N
(b)
zero
(c)
10N
(d)
20N
Two spheres A and B of exactly same mass are given equal positive and negative charges respectively. Their
masses after charging
(a)
remain unaffected
(b)
mass of A > mass of B
(c)
mass of A < mass of B
(d)
nothing can be said.
-10
An ebonite rod acquires a negative charges of 3.2  10 C. The number of excess electrons it has is
(a)
2  109
(b)
2  10-9
(c)
2  10-29
(d)
2  1029
2
Answer
Coulomb’s Law
1.
6.
(c)
(c)
2.
7.
(b)
(d)
3.
8.
(c)
(a)
4.
9.
(b)
(b)
5.
(d)
10.
(a)
11.
(a)
12.
(a)
13.
(b)
14.
(b)
15.
(d)
16.
(c)
17.
(c)
18.
(a)
19.
(d)
20.
(d)
21.
(a)
22.
(d)
23.
(b)
24.
(d)
25.
(a or all)
26.
(c)
27.
(c)
28.
(b)
29.
(c)
30.
(a)
3
Electric field
Q.1
Q.2
Q.3
A table–tennis ball which has been covered with a conducting paint is suspended by a silk thread so that it
hangs between two metal plates. One plate is earthed. When the other plate is connected to a high voltage
generator, the ball
(a)
is attracted to the high voltage plate and stays there
(b)
hangs without moving
(c)
swings backward and forward hitting each plate in turn
(d)
is repelled to the earthed plate and stays there
Five balls numbered 1 to 5 are suspended using separate threads. Pairs (1, 2), (2, 4) and (4, 1) show
electrostatic attraction while pairs (2, 3) and (4, 5) show repulsion. Then
(a)
Ball – 1 is positively charged
(c)
Ball – 1 is neutral
(d)
Ball – 1 is positively charged and Ball – 2 is negatively charged
Q.10
(d)
K2 : 1
q/q’=2
(b)
q/q’=1
(c)
q/q’= 4
(d)
q/q’=3
2.2  10-4N
(b)
4.410-4N
(c)
8.910-4N
(d)
17.610-4N
decreases
(b)
increases
the magnitude of its charge
both magnitude of its charge and its position
(b)
(d)
the position where it is situated
the magnitude of + q
The charge +q are placed at the four corners of a square. How much charge must be placed at its centre so that
the whole system is in equilibrium?
–q/4 (1+22)
(b)
–q/2 (1+22)
(c)
–q/8 (1+22)
(d)
+q/4 (1-22)
An electron (mass=9.110-31kg) and charge = 1.610-19C is sent in an electric field of intensity 1106V/m.
How long would it take for the electron, starting from rest to attain one-tenth velocity of light?
(a)
1.7  10-12s
(b)
1.7  10-6 s
(c)
1.7  10-8 s
(d)
1.710-10 s
An electron of mass Me, initially at rest, moves through a certain distance in a uniform electric field in time t 1.
A proton of mass Mp also initially rest, takes time t2 to move through an equal distance in this uniform electric
field. Neglecting the effect of gravity, the ratio t2/t1 is nearly equal to
(a)
Q.11
1 : K2
(c)
remain unchanged
(d)
nothing can be said as sufficient information is not available
A negatively charged particle is situated on a straight line joining two other stationary particles each having
charge + q. The direction of motion of negatively charged particle will depend on
(a)
Q.9
(c)
A soap bubble is given a negative charge. Then its radius
(a)
(c)
Q.8
K:1
A pendulum bob of mass 80 mg and carrying a charge of 210 C is at rest in horizontal uniform electric field
of 20,000V/m. The tension in the thread of the pendulum is
(a)
Q.7
(b)
-8
(a)
Q.6
1:K
A certain charge Q is divided at first into two parts q and q’. Later on, the charges are placed at certain
distance. If the force of interaction between two charges is maximum, then
(a)
Q.5
Ball – 1 is negatively charged
The ratio of the forces between two small spheres with constant charges, in air and in a medium of dielectric
constant K, is
(a)
Q.4
(b)
1
(b)
Mp / Me
(c)
Me / Mp
(d)
1836
X-rays
(c)
-rays
(d)
-particles
An electric field can deflect
(a)
neutrons
(b)
4
Q.12
Q.13
Q.14
The electric field that can balance a deutron of mass 3.2  10-27 kg is
(a)
19.6  10-10 N/C
(b)
19.6  10-8 N/C
(c)
19.6  1010 N/C
(d)
19.6  108 N/C
Electric lines of forces
(a)
exist everywhere
(b)
exist only in the immediate vicinity of electric charges
(c)
exist only when both positive and negative charges are near one another
(d)
are imaginary.
The dimensional formula of electric intensity
(a)
Q.15
Q.18
= F/q0
Q.20
Q.21
(b)
qE
(c)
ML2T-3A-1
(d)
ML2T-3A-2
> F/q0
(c)
< F/q0
(d)
none of the above.
(b)
6r
(c)
4/3r3 ( -0)
(d)
none of the above.
A proton and an electron are located in a uniform electric field. They will experience :
(a)
(b)
equal forces in same direction
forces equal in magnitude
(c)
equal acceleration in opposite directions
(d)
acceleration equal in magnitude.
A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will
be in equilibrium if q is equal to
(a)
Q.19
MLT-3A-1
A drop of oil of density  and radius r carries a charge q when placed in an electric field E, it moves upwards
with a velocity . If 0 is the density of air,  be the viscosity of the air, then which of the following forces is
directed up-wards
(a)
Q.17
(b)
A positive charged ball hangs from a silk thread. We put a positive test charge q 0 at a point and measure F/q0,
then it can be predicted that the electric field strength E will be
(a)
Q.16
MLT-2A-1
–Q/2
(b)
–Q/4
(c)
+Q/4
(d)
+Q/2
Two particles, each of mass m and carrying charge Q, are separated by some distance. If they are in
equilibrium under mutual gravitational and electrostatic forces then Q/m (in C/kg) is of the order of
(a)
10-5
(b)
10-10
(c)
10-15
(d)
10-20
Three point charges are placed at the corners of an equilateral triangle. Assume that only electrostatic forces
are acting
(a)
the system will be in equilibrium if the charges have the same magnitude but not all have the
same sign
(b)
the system will be in equilibrium if the charges have different magnitudes and not all have the
same sign
(c)
the system will be in equilibrium if the charges rotate about the centre of the triangle
(d)
the system can never be in equilibrium
Two identical pendulums, A and B, are suspended from the same point. The bobs are given positive charges,
with A having more charge than B. They diverge and reach equilibrium, with A and B making angles 1 and
2 with the vertical respectively.
(a)





b)

(c)




(d)
the tension in A is greater than that in B
5
Q.22
In a rectangular polygon of n sides, each corner is at a distance r from the centre. Identical charges of
magnitude Q are placed at (n-1) corners. The field at the centre is
(a)
Q.23
kQ/r2
(n-1)kQ/r2
(b)
(c)
n/n-1 k Q/r2
(d)
n-1 /nk Q/r2
Two identical metal balls with charges +2Q and –Q are separated by some distance, and exert a force F on
each other. They are joined by a conducting wire, which is then removed. The force between them will now
be
(a)
F
(b)
F/2
(c)
F/4
(d)
F/8
Electric Filed
ANSWER
1.
(c)
2.
(c)
3.
(b)
4.
(b)
5.
(c)
6.
(c)
7.
(b)
8.
(a)
9.
(d)
10.
(b)
11.
(d)
12.
(b)
13.
(d)
14.
(b)
15.
(b)
16.
(a)
17.
(b)
18.
(b)
19.
(b)
20.
(d)
21.
(c)
22.
(a)
23.
(d)
6
Dipole
Q.1
Q.2
Q.3
Q.4
Q.5
Q.6
Q.7
Electric charges q, q and –2q are placed at the corners of an equilateral triangle of side l. The magnitude of
electric dipole moment of the system is
[CPMT-1994]
(a)
ql
(b)
2q l
(c)
3q l
(d)
4q l
The electric potential at a point on the axis of an electric dipole depends on the distance r of the point from the
dipole as :
(a)
1/r
(b)
1/r2
(c)
r
(d)
1/r3
When a test charge is brought from infinity along the perpendicular bisector of the electric dipole the work done is
:
(a)
Positive
(b)
Negative
(c)
Zero
(d)
None of the above
An electric dipole has charges +q and –q at a separation r. At distant d > > r along the axis of the dipole, the field
is proportional to :
(a)
q/d2
(b)
qr/d2
(c)
q/d3
(d)
qr/d3
A given charged situated at a certain distance from an electric dipole in the end on position experiences a force F.
If the distance of the charge is doubled, the force acting on the charge will be :
[MNR-86]
(a)
2F
(b)
F/2
(c)
F/4
(d)
F/8
In case of a dipole filed
(a)
Intensity can be zero
(b)
Potential can be zero
(c)
Both can be zero
(d)
None can be zero.
Two point charges +q & -q are held fixed at (-d, 0) & (d, 0) respectively for (x, y) co-ordinate system then
[IIT-95]
Q.8
Q.9
Q.10
Q.11
Q.12
Q.13
Q.14
Q.15
(a)
the electric field E at all point on the x-axis has the same direction
(b)
E at all points of y-axis is along i
(c)
Work has to be done bringing a test charge from infinity to the origin
(d)
The dipole moment is 2 qd along –i.
An electric dipole placed in a uniform electric field experience, in general
[CPMT-1993]
(a)
A force and a torque
(b)
A force only
(c)
A torque only
(d)
Neither a force nor a torque.
When an electric dipole is placed in a uniform electric field a couple acts on it. The moment of couple will be
maximum when the dipole is placed :
(a)
Along the direction of the filed
(b)
Perpendicular to the direction of the field
(c)
Against the direction of the field
(d)
Inclined at an angle of 45 to the direction of the field
The work done in deflecting a dipole through 180 from direction is :
(a)
pE
(b)
2pE
(c)
1/2pE
(d)
Zero
At point on the axis of an electric dipole :
(a)
The electric field E is zero
(b)
The electric potential V is zero
(c)
Neither E nor V is zero
(d)
Both E and V is zero
The force of attraction between two coaxial electric dipoles whose centers are r in apart varies with distances as :
(a)
r-1
(b)
r-2
(c)
r-3
(d)
r-4
The electric intensity due to a dipole of length 10 cm and having a charged of 500 C, at point on the axis 20 cm
from one of the charges in air is :
(a)
9.28  107 N/C
(b)
20.5  107 N/C
7
(c)
6.25  10 N/C
(d)
13.1  1011 N/C
The torque  acting on an electric dipole of moment p in an electric field E is :
(a)
 = p. E
(b)
=pE
(c)
 = pE
(d)
 = pE
An electric dipole placed in an non-uniform electric field experiences:
(a)
A force but not a torque
(b)
A torque but not a force
(c)
A force and a torque
(d)
Neither a force nor a torque
7
Q.16
Q.17
Q.18
Q.19
Q.20
Q.21
An electric dipole consists of two opposite charges each of magnitude 1.0 C separated by a distance of 2.0 cm.
The dipole is placed in an external field of 1.0  105 N/C. The maximum torque on the dipole is :
(a)
0.2  10-3 N-m
(b)
2.0  10-3 N-m
-3
(c)
4.0  10 N-m
(d)
1.0  10-3 N-m
An electric dipole of moment p is placed at the origin along the x-axis. The electric field at a point P whose
position vector makes an angle  with the x-axis, will make an angle given by the following, where tan  = ½ tan
 --(a)

(b)

(c)
+
(d)
 + 2
An electric dipole placed with its axis at 30with a uniform electrical field experience a torque of magnitude 0.032
Nm. If the dipole were free to rotate, its potential energy in stable equilibrium would be
(a)
0.064J
(b)
–0.064J
(c)
0
(d)
–0.16J
A and B are two points on the axis and the perpendicular bisector respectively of an electric dipole. A and B are
far away from the dipole and at equal distances from it. The fields at A and B are EA and EB.
(a)
EA =EB
(b)
EA=2EB
(c)
EA=-2EB
(d)
EB =1/2  EA and EB is perpendicular to EA
In the previous question, let VA and VB be the potentials at A and B respectively
(a)
VA =VB
(b)
VA=2VB
(c)
VA O, VB= 0
(d)
VA= 0, VB= o
An electric dipole is placed at the origin and is directed along the x-axis. At a point P, far away from the dipole,
the electric field is parallel to the y-axis. OP makes an angle  with the x-axis
(a)
tan  =3
(b)
tan  =2
o
(c)
 = 45
(d)
tan =1/2
Answers
Dipole
1.
(c)
2.
(b)
3.
(c)
4.
(d)
5.
(d)
6.
(b)
7.
(b,d)
8.
(c)
9.
(b)
10.
(b)
11.
(c)
12.
(d)
13.
(c)
14.
(b)
15.
(c)
16.
(b)
17.
(b)
18.
(b)
19.
(c)
20.
(c)
21.
(acd)
8
Gauss’s Law
Q.1
Q.2
Q.3
Q.4
A cylinder of radius R and length l is placed in a uniform electric field E parallel to the cylinder axis. The
total flux for the surface of the cylinder is given by :
(a)
2R2E
(b)
2R2/E
(c)
(R2 + R2)/E
(d)
zero.
A charge is placed at the center of a cube with side L. The electric flux linked with cubical surface is :
[CPMT 1993]
(a)
(Q/6L20)
(b)
(Q/L20)
(c)
(Q/0)
(d)
zero.
A charge Q is situated at the center of a cube. The electric flux through one of the faces of the cube is :
(a)
(Q/0)
(b)
(Q/20)
(c)
(Q/40)
(d)
(Q/60).
Total electric flux coming out of a unit positive charge put in air is:
(a)
Q.5
Q.7
(b)
0-1
(c)
(40)-1
(d)
40.
A charge body has an electric flux  associated with it. They body is now placed inside a metallic container.
The electric flux 1 outside the container will be
(a)
Q.6
0
1 = 0
(b)
0 < 1 < 
(c)
1 = 
(d)
1 > .
In a region space having a uniform electric field E, hemispherical bowl of radius r is placed. The electric flux
 through the bowl is
(a)
2 r E
(b)
4 r2 E
(c)
2 r2 E
Positive electric flux indicates that electric lines of force are directed
(a)
outwards
(b)
inwards
(c)
outwards or inwards
(d)
 r2 E.
(d)
none
of
these.
Q.8
Number of electric lines of force emanating from 1 C of positive charge in a dielectric medium of constant 10
is
(a)
Q.9
Q.10
(c)
1/4  9  109 (d)
double
(b)
four times
(c)
zero
(d)
none of these.
1.13  1011.
The electric flux over a sphere of radius 1m is . If radius of the sphere were doubled without changing the
charge enclosed, electric flux would become
2
(b)
/2
(c)
/4
(d)
.
Electric field intensity at a point due to an infinite sheet of charge having surface charge density  is E. If
sheet were conducting electric intensity would be
E/2
(b)
E
(c)
2E
(d)
4E.
In a certain region of surface, there exists a uniform electric field of 2  103 k V/m. A rectangular coil of
dimensions 10 cm  20 cm is placed in x-y plane. The electric flux through the coil is
(a)
Q.13
9  109
(a)
(a)
Q.12
(b)
A sphere of radius 1m encloses a charge of 5C. Another charge of -5C is placed inside the sphere. The net
electric flux would be
(a)
Q.11
8.85  10-12
zero
(b)
30 V-m
(c)
40 V-m
(d)
50 V-m.
Two charged metallic sphere are joined by a very thin metal wire. If the radius of the larger sphere is twice
that of the smaller one, the electric field near the larger sphere is
(a)
twice that near the smaller sphere
(b)
half of that near the smaller sphere
(c)
the same as that near the smaller sphere
(d)
one-fourth of that near the smaller sphere
9
Q.14
A point charge Q is placed outside a hallow spherical conductor of radius R, at a distance r ( r>R) from its
centre C. the filed at C due the induced charges on the conductors is
(a)
zero
(b)
k Q/(r-R)2
2
(c)
k Q/r , directed towards Q
(d)
kQ/r2, directed away from Q
A positive point charge, which is free to move, is placed inside a hollow conducting sphere with negative
charge, away from its centre. It will
(a)
move towards the centre
(b)
move towards the nearer wall of the conductor
(c)
remain stationary
(d)
oscillate between the centre and the nearer wall
In a region of space, the electric field is in the x –direction and proportional to x,i.e., E =Eox î. Consider an
imaginary cubical volume of edge a, with its edges parallel to the axes of coordinates. The charge inside this
volume is
Q.15
Q.16
(a)
zero
(b)
ℇoEoa3
(c)
1/ℇoEoa3
(d)
1/6 ℇoEoa2
A charge Q is placed at the mouth of a conical flask. The flux of the electric field through the flask is
Q.17
(a)
zero
(b)
Q/ℇo
(c)
Q/2ℇo
(d)
< Q/2ℇo
A long string with a charge of  per unit length passes through an imaginary cube of edge a. the maximum
flux of the electric field through the cube will be
Q.18
(a)
Q.19
a/ℇo
(b)
2a /ℇo
6a2 /ℇo
(c)
(d)
3 a/ℇo
If the electric field id given by 6i + 3j + 4k, calculate the electric flux through a surface of area 20 units lying
in YZ-plane.
(a)

(b)
100
(c)
120
(d)
40.
Answer
(Gauss’ Law)
1.
(d)
2.
(c)
3.
(d)
4.
(b)
5.
(c)
6.
(c)
7.
(a)
8.
(d)
9.
(c)
10.
(d)
11.
(c)
12.
(c)
13.
(c)
14.
(c)
15.
(c)
16.
(b)
17.
(c)
18.
(d)
19.
(c)
10
Electric Potential
Q.1
The ratio of the forces between two small spheres charged to constant potential in air and in a medium of
dielectric constant K is
(a)
Q.2
Q.6
Q.8
Q.9

(b)
0
(c)
q/40
(d)
A
(b)
B
(c)
C
(d)
0
(b)
2/40 Q2/a
(c)
2/0 Q2/a
the p.d. between the points x = 1 and x = -2 is –15 V
(b)
the force on +1C charge at x =-1m is 10N
(c)
the work done in carrying +1C charge from origin to x =1 is 6J
(d)
the field near the origin is uniform, along x-axis
K2 : 1
the
2q/40
D
(d)
Q2/20a
A hollow charged metal sphere has radius R. If the potential difference between its centre and a point at a
distance 3R from the centre is V. the electric field intensity at distance 3R from centre, is
V/6R
(b)
V/4R
(c)
V/3R
(d)
V/2R
A charge Q is distributed over two concentric hollow spheres of radii r and R (>r) such that the surface
densities are equal. The potential at the common centre is
(a)
1/40. Q. (R2+r2)/ (R + r)
(b)
1/40. Q/ (R+r)
(c)
0
(d)
1/40. Q. (r+ R) (r2+ R2)
A hollow metal sphere of radius 5cm is charged such that the potential on its surface is 10V. The potential at
the centre of the sphere is
(a)
0V
(b)
10V
(c)
(d)
same as at point 5cm away from the surface
same as at point 10cm away from the surface
A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow
spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer
surface of the hollow shell be V. If the shell is now given a charge of -3Q, the new potential difference
between the two surfaces is
V
(b)
2V
(c)
4V
(d)
-2V
Two concentric metallic shells of radii R1 and R2 (>R1) have charges Q1 and Q2 respectively, the potential at a
distance r, where R1< r <R2, is 1/4o multiplied by
(a)
Q.11
(d)
(a)
(a)
Q.10
1 : K2
The electric potential in a region along the x – axis varies with x according to the relation V (x) = 3 +5x2.
Then
(a)
Q.7
(c)
For equal charges each of Q coulombs are placed at the four corners of a square of side a meters. The work
done in removing a charge –Q coulombs from its centre to infinity is
(a)
Q.5
K:1
In a certain region an uniform field E = Ex i exists. If a small circle is drawn with the origin as the centre
cutting the axes at A (a, 0), B (0, a), C (-a, 0) and D (0,-a), the potential is maximum at
(a)
Q.4
(b)
An infinite number of electric charges each equal to +q are placed at x = 1, 2, 3, 4, 8 …… so on. Find
potential at x = 0.
(a)
Q.3
1:K
Q1+Q2/r
(b)
Q1/R1+Q2/R2
(c)
Q1/r+Q2/R2
(d)
Q1/R2+Q1/R2
Two identical thin rings, each of radius R metres are coaxially placed at a distance R metres apart. If Q1
coulomb and Q2 coulomb are respectively the charges uniformly spreads on the two rings, the work done in
moving a charge q from the centre of one ring to that of the other is
11
(a)
0
(b)
1/40 . q(Q1 – Q2) /.R (2 – 1) / 2
(c)
1/40 . 2q(Q1 + Q2) / R
(d)
1/40 . q(Q1 + Q2) /R (2+1) / 2
Q.12
A half ring of radius R has a charge of  per unit length. The potential at the centre of the half ring is
(a)
k /R
(b)
k R
(c)
k /R
(d)
k
Q.13
Charge Q is given a displacement ŕ =aî + bĵ in an electric field E = E1î +E2ĵ. The work done is
Q.14
Q.15
Q.16
(a)
Q(E1a+E2b)
(b)
Q(E1a)2+(E2b)2
(c)
Q(E1+E2) a2+b2
(d)
Q(E21+E22) a2+b2
Let Vo be the potential at the origin in an electric field E=Exî +Eyĵ. The potential at the point (x,y) is
(a)
Vo-xEx-yEy
(b)
Vo+xEx+yEy
(c)
xEx+yEy-Vo
(d)
(x2+y2) E2x+E2y-Vo
The electric potential V at any point x,y,z (all in metres) in space is given by V = 4x 2 volts. The electric field
(in V/m) at the point (1m, 0, 2m) is
(a)
-8 î
(b)
8î
(c)
-16
(d)
85
A no conducting ring of radius 0.5 m carries a total charge of 1.11  10-10C distributed no uniformly on its
circumference, producing an electric field E everywhere in space. The value of the line integral
∫∫=0∫ =  -E. d∫ (∫ = 0 being the centre of the ring) in volts is
(a)
Q.17
+2
(b)
–1
(c)
–2
(d)
0
A charge +q is placed at each of the points x =xo, x =5xo,….ad infinitum on the x-axis, and a charge –q is
placed at each of the points x =2xo,x =4xo, x =6x0…ad infinitum. Here, xo is a positive constant. Take the
electric potential at a point due to a charge Q at a distance r from it to be Q/(4ℇor). Then, the potential at the
origin due to the above system of charges is
Q.18
(a)
0
(b)
q / 8ℇoxo 1n 2
(c)

(d)
q 1n 2/4 ℇoxo
A solid sphere of radius R is charged uniformly. At what distance from its surface is the electrostatics
potential half of the potential at the centre?
(a)
Q.19
Q.20
Q.21
R
(b)
R/2
(c)
R/3
(d)
2R
A large solid sphere with uniformly distributed positive charge has a smooth narrow tunnel through its centre.
A small particle with negative charge, initially at rest far from the sphere, approaches it along the line of the
tunnel, reaches its surface with a speed v, and passes through the tunnel. Its speed at the centre of the sphere
will be ?
(a)
0
(b)
v
(c)
2v
(d)
1.5v
Which of the following is not true for a region with a uniform electric field?
(a)
it can have free charges
(b)
it may have uniformly distributed charged
(c)
it mat contain dipoles
(d)
none of the above
‘All charge on a conductor must reside only on its outer surface’. This statement is true
(a)
in all cases
(b)
for spherical conductors only (both solid and hollow)
(c)
for hollow spherical conductors only
(d)
for conductors which do not have any sharp points or corners
12
Q.22
Q.23
Q.24
Q.25
Q.26
Q.27
Q.28
A spherical conductor A of radius r is placed concentrically inside a conducting shell B of radius R (R>r).A
charge flowing from A to B will be
(a)
Q [ R/R + r ] (b)
Q [ r/R + r]
(c)
Q
(d)
zero
A spherical equipotential surface is not possible
(a)
for a point charge
(b)
for a dipole
(c)
inside a uniformly charged sphere
(d)
inside a spherical capacitor
In a certain charge distribution, all points having zero potential can be joined by a circle S. Points inside S
have positive potential, and points outside S have negative potential. A positive charge, which is free to move,
is placed inside S
(a)
it will remain in equilibrium
(b)
it cam move inside S, but it cannot cross S
(c)
it must cross S at some time
(d)
it may move, but will ultimately return to its starting point
If the earth’s surface is treated as a conducting surface with some charge, what should be the order of
magnitude of the charge per unit area, in C/m2, so that a proton remains suspended in space near the earth’s
surface?
(a)
10-18
(b)
10-12
(c)
10-6
(d)
1
A simple pendulum of time period T is suspended above a large horizontal metal sheet with uniformly
distributed positive charge. If the bob is given some negative charge, its time period of oscillation will be
(a)
>T
(b)
<T
(c)
T
(d)
proportional to its amplitudes
A spring-block system undergoes vertical oscillation above a large horizontal metal sheet with uniform
positive charge. The time period of the oscillation is T. if the block is given a charge Q, its time period of
oscillation will be
(a)
T
(b)
>T
(c)
<T
(d)
>T of Q is positive and < T if Q is negative
A large flat metal surface has a uniform charge density +. An electron of mass m and charge e leaves the
surface at point A with speed u, and returns to it at point B. disregard gravity. The maximum value of AB is
(a)
Q.29
u2mℇo/e
(b)
u2eℇo/m
(c)
u2e/ℇo m
(d)
u2e/ℇom
Small drops of the same size are charged to V volt each. If n such drops coalesce to form a single
large drop, its potential will be :
(a)
Vn
(b)
V/n
(c)
Vn1/3
(d)
Vn2/3
Q.30. Sixty four equal charged drops are combined to form a big drop. If the potential on each drop is 10 volt, then
the potential of the big drop will be
(a)
10 V
(b)
40 V
(c)
13
160 V
(d)
640 V
ANSWER
Electric Potential
1.
(a)
2.
(d)
3.
(c)
4.
(c)
5.
(a), (b)
6.
(a)
7.
(d)
8.
(b)
9.
(a)
10.
(c)
11.
(b)
12.
(d)
13.
(a)
14.
(b)
15.
(b)
16.
(a)
17.
(b)
18.
(a)
19.
(c)
20.
(c)
21.
(c)
22.
(d)
23.
(c)
24
(b)
25.
(b)
26.
(c)
27.
(b)
28
(b)
29.
(d)
30.
(c)
14
Capacitor
Q.1
Q.2
Q.3
Q.4
A slab of copper of thickness d/2 is inserted in between the plates of a parallel plate capacitor, where
d is the separation between the two plates. If the capacity of the capacitor without copper slab is C
and with copper slab is C’ then C, / C. is
(a)
2
(b)
2
(c)
1
(d)
1/2
A parallel plate capacitor is made by stacking n equally spaced plates connected alternately. If the
capacitance between any two plates is C. Then the resultant capacitance is
(a)
C
(b)
nC
(c)
(n-1)C
(d)
(n+1)C
Eight drops of mercury of equal radii and possessing equal charges combine to form a big drop.
Then the capacitance of big drop compared to each individual drop is
(a)
8 times
(b)
4 times
(c)
2 times
(d)
32 times
A parallel plate capacitor is charged and then isolated. What is the effect on increasing the plate
separation?
(a)
(b)
(c)
(d)
Charge
Constant
Increase
Constant
Constant
Potential
Constant
Increase
Decrease
Increase
Capacitance
Decrease
Decrease
Increase
Decrease
Q.5
A 500 F capacitor is charged at a steady rate of 100C/s. The potential difference across the
capacitor will be 10V after an interval
(a)
5s
(b)
20s
(c)
25s
(d)
50s
Q.6
A 1F capacitor and 2F capacitor are connected in parallel across a 1200V line. The charged
capacitors are then disconnected from the line and from each other. These two capacitors are now
connected to each other in parallel with terminals of unlike signs together. The charges on the
capacitors will be
(a)
Q.7
Q.8
Q.9
1800C each
(b)
400C and 800C
(c)
800C and 400C
(d)
800C and 800C
In a charged capacitor, the energy resides in
(a)
the positive charges
(b)
both the positive and negative charges
(c)
the field between the plates
(d)
around the edges of capacitor plate
A parallel plate capacitor is charged to 160V. When a 2 mm thick dielectric slab is inserted in
between the plates the potential difference across the plates decreases, however if the distance
between the plates is increased by 1.6mm, the same potential difference is restored. The dielectric
constant of the material of the slab is
(a)
1.25
(b)
2.5
(c)
4
(d)
5
Two capacitors each having capacitance C and breakdown voltage V are joined in series. The
capacitance and breakdown voltage of combination is
(a)
2C and 2V
(b)
C/2 and V/2 (c)
2 C and V
(d)
C/2 and 2V
15
Q.10 A parallel plate capacitor of plate area A and plate separation d is charged to potential difference V
and then the battery is disconnected. A slab of dielectric constant K is then inserted between the
plates of the capacitor so as to fill the space between the plates. If Q, E and W denote respectively,
the magnitude of charge on each plate, the electric field between the plates (after the slab is
inserted), and work done on the system in question in the process of inserting the slab, then
(a)
Q = 0AV / d
(b)
Q = 0 KAV / d
(c)
E = v/K d
(d)
W = 0AV2 / 2d (1-1/K)
Q.11 A parallel plate air capacitor is connected to a battery. The quantities charge, voltage, electric field
and energy associated with this capacitor are given by Q0, V0, E0 and U0 respectively. A dielectric
slab is now introduced to fill the space between the plates with battery still in connection. The
corresponding quantities now given by Q, V, E and U are related of the previous one as
(a)
Q >Q0
(b)
V>V0
(c)
E >E0
(d)
U >U0
Q.12 The amount of heat liberated when a capacitor of C farads charges to a potential difference of V volts
is discharged through a resistor of R ohms is H joules. The same capacitor is now charged to a
potential difference of 2V and discharged through a resistor of 2R ohms, then heat liberated is
(a)
4H
(b)
2H
(c)
H
(d)
H/2
Q.13 The heat generated through 2 and 8 resistance separately when a capacitor of 200F capacity
charged to 200V is discharged one – by – one will be
(a)
4J and 16J respectively
(b)
16J and 4J respectively
(c)
4J and 8J respectively
(d)
4J and 4J respectively
Q.14 Six identical capacitors each of 1F are joined is parallel and the combination is put across a battery
of emf 2V. Now the battery is disconnected and the capacitors are joined is series. The total energy
and potential difference across the series combination is
(a)
2J and 2V (b)
2J and 12V (c)
12J and 2V (d)
12J and 12V
Q.15 Suppose n identical capacitors are joined in parallel and charged to potential V. Now they are
separated and joined in series. If the energy possessed by each capacitor is U, then on joining them
in series, the energy and potential difference for the combination are
(a)
nU, V
(b)
U, n V
(c)
nU, nV
(d)
less than nU, nV
Q.16 A parallel plate capacitor with a dielectric constant K=3 filling the space between the plates is
charged to a potential difference V. The battery is then disconnected and the dielectric slab having
K=2. The ratio of energy stored in the capacitor before and after replacing the dielectric slab by now
one is
(a)
3:2
(b)
9:4
(c)
4:9
(d)
2:3
Q.17 A capacitor of capacity C1 is charged to a potential V0. The electrostatic energy stored in it is U0. It is
connected to another unchanged capacitor of capacitance C2 in parallel. The energy dissipated in the
process is
(a)
C2 / C1+C2 U0
(b)
C1 / C1+C2 U0
2
(c)
[C1- C2 / C1 + C2] U0
(d)
C1 C2 / 2 (C1 + C2)U0
Q.18 A parallel plate capacitor is connected to a battery. The plates are pulled apart with a uniform speed.
If x is the separation between the plates then the time rate of change of electrostatic energy of the
capacitor is proportional to
(a)
x2
(b)
x
(c)
1/x
(d)
1/x2
Q.19
If we treat the earth as a conducting sphere of radius 6400km, its capacitance would be of the order of
16
Q.20
Q.21
Q.22
Q.23
(a)
1F
(b)
1mF
(c)
1F
(d)
103F
When two uncharged metal balls of radius 0.09 mm each collide, one electron is transferred between them.
The potential difference between them would be
(a)
16V
(b)
16pV
(c)
32V
(d)
32pV
A conducting sphere of radius R, and carrying Q, is joined to an uncharged conducting sphere of radius 2R.
The charge flowing between them will be
(a)
Q/4
(b)
Q/3
(c)
Q/2
(d)
2Q/3
A capacitor of capacitance C is charged to a potential difference V form a cell and then disconnected from it.
A charge +Q is now given to its positive plate. The potential difference across the capacitor is now
(a)
V
(b)
V+ Q/C
(c)
V+Q/2C
(d)
V –Q/C, if V <CV
A capacitor is connected to a cell of emf ℰ and some internal resistance. The potential difference across the
(a)
Q.24
Q.25
Q.26
Q.27
Q.28
Q.29
Q.30
cell is ℰ
(b)
cell is < ℰ
(c)
capacitor is <ℰ
(d)
capacitor is >ℰ
In a parallel –plate capacitor of capacitance C, a metal sheet is inserted between the plates, parallel to them.
The thickness of the sheet is half of the separation between the plates. The capacitance now becomes
(a)
4C
(b)
2C
(c)
C/2
(d)
C/4
Two capacitors of capacitance 3F and 6F are charged to a potential of 12V each. They are now connected
to each other, with the positive plate of each joined to the negative plate of the other. The potential difference
across each will be
(a)
zero
(b)
3V
(c)
4V
(d)
6V
Let ua and ud represent the energy density (energy per unit volume) in air and in a dielectric respectively, for
the same field in both. Let K = dielectric constant. Then,
(a)
ua= ud
(b)
ua= Kud
(c)
ud = Kua
(d)
ua=(K-1) ud
In a parallel –plate capacitor, the region between the plates is filled by a dielectric slab. The capacitor is
charged from a cell and then disconnected from it. The slab is now taken out
(a)
some charge is drawn from the cell
(b)
some charge is returned to the cell
(c)
the potential difference across the capacitor is reduced
(d)
no work is done by an external agent in taking the slab out
In a parallel –plate capacitor, the region between the plates is filed by a dielectric slab. The capacitor is charge
from a cell and then disconnected from it. The slab is now taken out
(a)
the potential difference across the capacitor is reduced
(b)
the potential difference across the capacitor is increased
(c)
the energy stored in the capacitor is reduced
(d)
no work is done by an external agent in taking the slab out
In order to obtain a time constant of 10 seconds in an RC circuit containing a resistance of 103 , the capacity
of a condenser should be :
(a)
10F
(b)
100F
(c)
1000F
(d)
10,000F.
A parallel plate capacitor is connected to a battery. The plates are pulled apart with a uniform speed. If x is the
separation between the plates then the time rate of change of electrostatic energy of the capacitor is
proportional to
(a)
x2
(b)
x
(c)
1/x
(d)
1/x2
17
ANSWER
Capacitor
1.
(b)
2.
(c)
3.
(b)
4.
(d)
5.
(d)
6.
(b)
7.
(c)
8.
(d)
9.
(a), (c), (d)
10.
(a), (d)
11.
(d)
12.
(a)
13.
(d)
14.
(d)
15.
(c)
16.
(d)
17.
(a)
18.
(d)
19.
(b)
20.
(c)
21.
(d)
22.
(d)
23.
(d)
24.
(a,c,d)
25.
(a)
26.
(c)
27.
(b)
28.
(b)
29.
(d)
30.
(d)
18
Current Electricity
Q.1
A cell if enf 1,5 V gives a currernt of 15 A when connected directly to an ammter of 004  resistance. The
internal resistance of the cell is :
(a)
Q.2
Q.7
zero
random error
1. 0 
(b)
1.50
(c)
1.00
(d)
1.20
(b)
2E
(c)
E/2
(d)
E/4
(b)
2  10-3 V
(c)
4  10-3 V
(d)
2  10-1V
(b)
1A
(c)
1. 5 A
(d)
2.5 A
(b)
inside error
(c)
error due to thermo-electric effect
A potentiometer wire of cross-sectional area 8  10-6 m2 carries a current of 0.2 A. The resistivity of the material
of the wire is 4  10-7 -m. The potential gradient along the wire is :
0.01 V/m
(b)
10 V/m
(c)
1.6  10-2 V/m (d)
5 V/ m
The driver cell o a potentiometer is of emf 2.0 V and negligible internal resistance. The potentiometer wire AB is
1.0 m long and has a resistance of 5.0 . The resistance to be connected in series with the wire AB os as to have a
potential drop of 5 mV across the whole wire is :
1985
(b)
1990 
(c)
1995 
(d)
2000 
Two cells are first combined so as to support each other and then so as to oppose each other. These combinations
of cells balance on a potentiometer wire at length 60 cm and 30 cm respectively. The ratio of the emf of the cells
is :
2:1
(b)
3:1
(c)
1:1
(d)
4:1
A battery of 20 cells, having emf of 1.8 V and internal resistance 0.1  is charged by a charging current of 15 A.
The chemical power stored is
90 W
(b)
990 W
(c)
540 W
(d)
450 W
There are 24 cells, each of emf 2 V and internal resistance 0.4 . They are arranged in 4 rows, each containing 6
cells in series, the rows are connected in parallel. What should be the resistance of the load so that this battery of
cells gives maximum current?
(a)
Q.12
4  10-1 V
(d)
(a)
Q.11
E
end errors
(a)
Q.10
1.35
(a)
(a)
Q.9
(d)
In the measurement of resistance by a meter bridge, the known and the unknown resistance are interchanged to
eliminate
(a)
Q.8
0.1 
A student connects four cells, each of emf 1.5 V and internal resistance 0.25, in series but one cell has its
terminals reversed. This battery sends current in a 2  resistor. The current is :
(a)
Q.6
(c)
A voltmeter of 998  resistance is joined to a cell or emf 2 V and internal resistance 2 . The error in the
measurement of emf will be :
(a)
Q.5
0.06 
A cell of emf E and internal resistance r is connected to an external resistance r. The p.d. across the terminals of
the cells is :
(a)
Q.4
(b)
A current of 2.0 A passes through a cell of emf 1.5 V having internal resistance of 0.15 . The potential
difference across the terminals of the cell in volt is:
(a)
Q.3
0.04 
0
(b)
0.1 
(c)
0.6 
(d)
2.4 
There are 24 cells, each of emf 2 V and internal resistance 0.4 . They are arranged in 4 rows, each containing
6 cells in series; the rows are connected in parallel. What should be the resistance of the load so that this battery of
cells gives maximum power?
19
(a)
Q.13
Q.14
(c)
m = 1, n = 24
(d)
m = 2, n = 12
m = 6, n = 4
(b)
m = 4, n = 6
(c)
m = 3, n =8
(d)
m = 8, n =3
The deflection of a galvanometer falls from 50 to 10 divisions when a shunt of 5  is connected across it. The
resistance of galvanometer is
20 
(b)
25 
(c)
40 
(d)
10 
A voltmeter has a range of 5.0 V and bears specification 2000 /V. The additional resistance needed to convert it
into a voltmeter of 15 V range is
4000 
(b)
6000 
(c)
100000 
(d)
20000 
A resistance R = 1980  in connected in series with a voltmeter, after which the scale division become n = 100
times larger. The resistance of the voltmeter before putting the resistance R was
100 
(b)
20 
(c)
2000 
(d)
200 
If the voltage across a bulb drops by 5% of its rated value, the power will decrease by what percentage of the
rated value.
5%
(b)
10%
(c)
20%
(d)
25%
One heater boils certain amount of water in 10 minutes and another heater in 15 minutes. In how much time the
same water will be boiled if the two heaters are put in series?
2.5 min
(b)
6 min
(c)
12.5 min
(d)
25 min
One heater boils certain amount of water in 10 minutes and another heater in 15 minutes. In how much time the
same water will be boiled if the two heaters are put is parallel ?
(a)
Q.21
2.4 
There are 24 cells, each of emf 2 V and internal resistance 0.4 . What should be the number m of rows and
number n of cells in each row so that the maximum current is delivered in a load of resistance 0.6 
(a)
Q.20
(d)
m = 4, n = 6
(a)
Q.19
0.6 
(b)
(a)
Q.18
(c)
m = 6, n = 4
(a)
Q.17
0.1 
(a)
(a)
Q.16
(b)
There are 24 cells, each of emf 2 V and internal resistance 0.4 . What should be the number m of rows and
number n of cells in each row so than the power through a load of 2.4  is maximum
(a)
Q.15
0
2.5 min
(b)
6 min
(c)
12.5 min
(d)
25 min
Two resistors R1 and R2 may be connected either in series or in parallel across a battery of emf  having negligible
internal resistance. If the joule heating for the parallel combination is to be four times that for the series
combination, the for R1 = 100 , R2 must be
(a)
400 
(b)
25 
(c)
200 
(d)
100 
*Q.22 Two bulbs A and B, one of resistance R and the other of resistance r (r < R) respectively are connected in turn in
series and parallel. A voltage V is applied across the combination. Then,
Q.23
(a)
In series arrangement, A is brighter than B
(b)
In series arrangement, B is brighter than A
(c)
In parallel arrangement, A is brighter than B
(d)
In parallel arrangement, B is brighter than A
Three resistor 10 k, 1 W ; 20 k, ½ W and 40 k, ¼ W are joined in series. The current in the combination
should not exceed
(a)
1 mA
(b)
2 mA
(c)
20
3 mA
(d)
4 mA
Q.24
Drift velocity vd varies with the intensity of electric field as per the relation
vd  E
(a)
Q.25
(b)
vd  1/E
(c)
vd = constant
(d)
vd  E2
The drift velocity of the electrons in a copper wire of length 2m under the application of a potential difference of
200 V is 0.5 ms-1. Their mobility is (in m2V-1s-1)
(a)
2.5  10-3
(b)
2.5  10-2
(c)
5  10
(d)
5  10-3
The electron drift speed is small and the charge of the electron is also small but still we obtain large current in a
conductor. This is due to
Q.26
(a)
The conducting property
(b)
The resistance of the conductor is small
(c)
The electron number density of the conductor is small
(d)
The electron number density of the conductor is enormous
Q.27
Whetstone Bridge is more accurate method of measuring the resistance because
(a)
it has four resistor arms
(b)
it is based on Kirchoff’s laws
(c)
it does not involve Ohm’s law
(d)
it is a null method.
Q.28
In a potentiometer, the length and resistance of the wire are 10 metre and 20 respectively. The wire is connected
in series with a resistance of 5  and a battery of e.m.f. 5 volt and negligible internal resistance. The potential
gradient along the wire in volt per meter is
(a)
0.1
(b)
0.2
(c)
0.3
(d)
0.4
Q.29
A potentiometer consists of a wire of length 4m and resistance 10 . It is connected to a cell of e.m.f 2V. The
potential difference per unit length of the wire will be
(a)
Q.30
0.5 V/m
(b)
2 V/m
(c)
5 V/m
(d)
10 V/m
Ten identical electric bulbs, each rated 220 V, 50 W are used in parallel on 200 V line for 10 hours a day in month
of 30 days. The electric energy consumed in kWh is
(a)
5 kWh
(b)
50 kWh
(c)
150 kWh
(d)
1500 kWh
Current Electricity
1.
(b)
2.
(d)
3.
(c)
4.
(c)
5.
(a)
6.
(a)
7.
(c)
8.
(b)
9.
(b)
10.
(c)
11.
(a)
12.
(c)
13.
(d)
14.
(b)
15.
(a)
16.
(d)
17.
(b)
18.
(b)
19.
(d)
20.
(b)
21.
(d)
22.
(b,c)
23.
(b)
24.
(a)
25.
(d)
26.
(d)
27.
(d)
28.
(d)
29.
(a)
30.
(c)
21
Magnetism
Biot Savart law
Q.1
A vertical wire carries a current upwards. The magnetic field at a point due to north of the wore is directed
(a)
Q.2
Q.3
upward
(b)
due south
(c)
due west
(d)
due east
A length of wire carries a steady current. It is bent first to form a circular plane coil of one turn and it produces a
field of induction B. The same length is now bent more sharply to give a double loop of smaller radius. The
magnetic field at the centre caused by the same current is
(a)
1/4 B
(b)
2B
(c)
4B
(d)
1/2 B
Magnetic field B at the centre of a square ABC, of side a in which a current I enters the corner and leaves the
corner C is
(a)
42I /a
(b)
220I / 4a
(c)
0
(d)
220I / a
Force on a Wire
Q.4
Q.5
Q.6
A positive charge projected towards east is deflected towards north by a magnetic field. The field is directed :
(a)
towards west
(b)
towards south
(c)
upwards
(d)
downwards
Which of the following particles will experience maximum force when projected perpendicular to a magnetic
field with same velocity ?
(a)
electron
(b)
proton
(c)
He+
(d)
Li++
An electron accelerated through a potential difference V enters a uniform transverse magnetic field in which it
experiences a force F. If V be increased to 2V, the electron will experience a force :
(a)
Q.7
F/2
(b)
F/2
(c)
2 F
(d)
2F
An ion enters perpendicular to a uniform field of 4  10-2 Wb m-2 with a velocity 2  105 ms-1. If the specific
change (q/m) of the ion be 5  107 C kg-1 then the radius of its circular path will be :
(a)
0.10 m
(b)
0.40 m
(c)
0.20 m
(d)
0.25 m
Force on a Charge Particle
Q.8
Two particles X and Y having equal charges after being accelerated through the same potential difference enter a
region of uniform magnetic field and describe circular paths of radii R1 and R2 respectively. The ratio of mass of
X to that of Y is
(a)
Q.9
(c)
(R1 / R2)2
(d)
R1 / R2
25 keV
(b)
50 keV
(c)
100 keV
(d)
200 keV
1:1
(b)
2:1
(c)
1:2
(d)
1:4
A charged particle is moving in a circular path in a magnetic field. If the velocity of the charged particle suddenly
increase, which quantity remains unaltered?
(a)
Q.12
R2 / R1
A proton and an alpha particle having the same kinetic energy enter a uniform magnetic filed region at right
angles to it and traces circular paths of radii R1 and R2 respectively, then R1 : R2 is
(a)
Q.11
(b)
A deuteron of kinetic energy 50 keV is describing a circular orbit of certain radius in a magnetic field B. The
kinetic energy of a proton that describes a circular orbit of the same radius in the same field is
(a)
Q.10
(R1 / R2)1/2
kinetic energy (b)
momentum
(c)
radius
(d)
angular frequency
Particles having positive charges occasionally come with high velocity from the sky towards the earth at the
equator. On account of magnetic field of the earth, they would be deflected towards the
(a)
north
(b)
south
(c)
22
east
(d)
west
Q.13
A magnetic field of 5.0  10-4 T just balances a perpendicular electric field of 15 kV/m in their effect on an
electron beam passing through the two field in a direction perpendicular to both of them. What is the speed of the
electrons?
(a)
Q.14
(b)
3  104 m/s
(c)
7.5  104 m/s
(d)
3  107 m/s
A charged particle is released from rest in a region of steady and uniform electric and magnetic fields which are
parallel to each other. The particle will move in
(a)
Q.15
75 m/s
Straight line
(b)
Circle
(c)
Helix
(d)
Cycloid
A charged particle moves through a magnetic field in a direction perpendicular to it. Then the
(a)
(b)
velocity remains unchanged
speed of the particle remains unchanged
(c)
direction of the particle remains unchanged
(d)
accelerations remain unchanged
dQ.16 A particle of charge – 16  10-18 coulomb moving with velocity 10 m/s along the x-axis enters a region where a
magnetic field of induction B is along the y-axis, and an electric field of magnitude 104 V/m is along the negative
Z-axis. If the charged particle continues moving along the X-axis, the magnitude of B is
(a)
108 Wb/m2
(b)
105 Wb/m2
(c)
106 Wb/m2
(d)
103 Wb/m2
Magnetic Dipole and Earth’s-magnetism & Magnetic material
Q.17
Q.18
If the magnetic susceptibility of a specimen is small and positive, the specimen is :
(a)
Diamagnetic
(b)
Paramagnetic
(c)
Ferromagnetic
(d)
Non-magnetic.
If the magnetic moment of the atom of a substance is zero, the substance is called :
(a)
Diamagnetic
(b)
Paramagnetic
(c)
Q.19
Ferromagnetic
(d)
Antiferromagnetic.
(b)
Paramagnetism
(d)
none of the above.
(b)
(d)
Paramagnetic
Mercury.
Most of the substance show which of the following magnetisms :
(a)
(c)
Diamagnetism
Ferromagnetism
bQ.20 An example diamagnetic substance is :
(a)
(c)
Q.21
Q.22
Above Curie point, a ferromagnetic material becomes :
(a)
Non-magnetic
(b)
Neon
(c)
Paramagnetic
(d)
Strongly ferromagnetic.
Which one of the following materials is ferromagnetic ?
(a)
Q.23
Gold
(b)
Nickel
(c)
Wood
(d)
Manganese
The magnetic field lines :
(a)
(b)
(c)
(d)
Q.24
Aluminium
Solution of iron salt
intersect at the neutral point
intersect near north and south poles
cannot intersect at all.
Depend upon the position of the magnet.
A bar magnet is placed inside a non-uniform magnet field. It experiences :
(a)
a force and torque
(b)
a force but not a torque
(c)
a force but not a force
(d)
neither a force nor a torque.
23
Q.25
Q.26
Q.27
Two bar magnets having same geometry with magnetic moments M and 2 M are firstly placed in such a way that
their similar poles are on the same side; then its period of oscillation is T1. Now the polarity of one of the magnets
is reversed. The time period of oscillations will be :
(a)
T1 < T2
(b)
T1 > T2
(c)
T1 = T2
(d)
T2 = .
Which of the following is most suitable for the core of the electromagnets ?
(a)
Air
(b)
Soft iron
(c)
Steel
(d)
Cu-Ni alloy.
A bar magnet of magnetic moment 80 units is cut into two halves of equal length, the magnetic moment of each
half will be :
(a)
Q.28
Q.29
(b)
40 units
(c)
60 units
(d)
20 units
Tesla is the unit
(a)
Magnetic flux
(b)
Magnetic intensity
(c)
Magnetic induction
(d)
Magnetic moment
If r be the distance of a point on the axis of a bar magnet from its center, then magnetic field at this point is
proportional to :
(a)
Q.30
80 units
(1/r)
(1/r2)
(b)
(c)
(1/r3)
(d)
(1/r4)
Points A and B are situated along the extended axis of a 2 cm long bar magnet at distance x and 2x cm
respectively from the pole nearer to the point. The ratio of the magnetic fields at A and B will be:
(a)
4 : 1 exactly
(b)
8 : 1 exactly
(c)
4 : 1 approximately
(d)
8 : 1 approximately.
Magnetism
1.
6.
11.
16.
21.
26.
(c)
(c)
(d)
(d)
(c)
(b)
2.
7.
12.
17.
22.
27.
(c)
(a)
(c)
(b)
(b)
(b)
3.
8.
13.
18.
23.
28.
(c)
(c)
(d)
(a)
(c)
(c)
24
4.
9.
14.
19.
24.
29.
(d)
(c)
(a)
(a)
(a)
(c)
5.
10.
15.
20.
25.
30.
(d)
(a)
(bc)
(b)
(a)
(d)
Electromagnetic Induction
Q.1
Q.2
Q.3
Q.4
Q.5
Q.6
Q.7
Q.8
Q.9
Q.10
Q.11
When the current through a solenoid increases at a constant rate, the induced current
(a)
is a constant and is in the direction of the inducing current
(b)
(c)
(d)
is a constant and is opposite to the direction of the inducing current
(b)
(c)
(d)
Current will decrease in each loop
Increases with time and is in the direction of inducing current
increases with time and is opposite to the direction of inducing current.
Two circular, similar, coaxial loops carry equal currents in the same direction. If the loops are brought nearer, what will
happen?
(a)
Current will increase in each loop
Current will remain same in each loop
Current will increase in one and decrease in the other
A solenoid has 2000 turns wound over a length of 0.3 m. The area of its cross-section is 1.2  10-3 m2. Around its central
portion a coil of 300 turns is wound. If an initial current of 2 amp in the solenoid is reversed in 0.25 sec, the e.m.f. induced in
the coil is equal to :
(a)
6  10-4 V
(b)
48 mV
(c)
6  10-2 V
(d)
48 kV
Two different loops are concentric and lie in the same plane. The current in the outer loop is clock wise and increases with
time. The induced current in the inner loop then is :
(a)
clockwise
(b)
zero
(c)
counterclockwise
(d)
in a direction that depends on the ratio of the loop radii
The north pole of a long horizontal bar magnet is being brought closer to a vertical conducting plane along the perpendicular
direction. The direction of the induced current in the plane will be :
(a)
horizontal
(b)
vertical
(c)
clockwise
(d)
anticlockwise
A step-down transformer transforms a supply line voltage of 2200 volt into 220 volt. The primary coil has 5000 turns. The
efficiency and power transmitted by the transformer are 90% and 8 kilowatt respectively. Then the number of turns in the
secondary is :
(a)
5000
(b)
50
(c)
500
(d)
5
The average e.m.f. induced in a coil when a current changes from 0 to 2A in 0.05 sec is 8V. The self-inductance of the coil is
:
(a)
0.1 H
(b)
0.2 H
(c)
0.4 H
(d)
0.8 H
A long metallic pipe is held vertical. A small bar magnet with its N-ole pointing downwards is allowed to fall through it.
After a lapse of some time, the magnet will be observed to be falling with an acceleration a where
(a)
a>g
(b)
a<g
(c)
a=g
(d)
a= 0
Two identical coaxial circular coils carry equal currents. When viewed from a point mid-way between the coils the direction
of current in one coil is clockwise and in the other it is anti-clockwise. If these coils approach each other, the current
(a)
in each coil increases
(b)
in each coil remains same
(c)
in each coil decreases
(d)
in one coil increases and in other coil decreases.
A small conducting circular coil is placed inside a long solenoid carrying a current. The plane of the coil contains the axis of
the solenoid. If the current in the solenoid is increased, the current induced in the coil is
(a)
clockwise
(b)
anti-clockwise (c)
zero
(d)
a.c.
A hundred turns of insulated copper wire are wrapped around an iron cylinder of area 1  10-3 m2 and are connected to a
resistor. The total resistance of the circuit is 10 . If the longitudinal magnetic induction in the iron changes 0.1 T in one
direction to 0.1 T in opposite direction, the charge that flows in the circuit is
25
Q.12
Q.13
(a)
2  10-3 C
(b)
1  10-3 C
(c)
2  10-6
(d)
zero
2
A closely would coil of 100 turns and area of cross-section 1 cm has a coefficient of self-inductance 1 mH. The magnetic
induction at the centre of the core of the coil when a current of 2A flows in it is
(a)
0.2 Wb/m2
(b)
0.4 Wb/m2
(c)
0.8 Wb/m2
(d)
1.0 Wb/m2
A conducting bar is pulled with a constant speed v on a smooth conducting rail. The region has a steady magnetic field of
induction B as shown in the figure. If the speed of the bar is doubled then the rate of heat dissipation will:
(a)
remain constant will
(b)
become quarter of the initial value
(c)
become four fold
(d)
get doubled
Q.14
A current I = 10 sin (100) is passed in first coil, which induces a maximum e.m.f. of 5 volt in second coil. The mutual
inductance between the coils is :
(a)
10mH
(b)
15mH
(c)
20 mH
(d)
5mH
Q.15
A solenoid of resistance 50 and inductance 5mH is connected to 200 V battery. Calculate maximum energy stored :
(a)
4 mJ
(b)
0.4 mJ
(c)
40 mJ
(d)
400mH
Alternate Current
Q.16
Q.17
Q.18
Q.19
Q.20
Q.21
Q.22
The rms value of alternating current which when passed through a resistor produces heat which is thrice that produced by the
current of 2 A in the same resistor, is
(a)
6A
(b)
2A
(c)
3.46 A
(d)
0.65 A
In a series LCR circuit, the p.d. across the resistor is 30 V, across the inductance 80 V and across the capacitance is 40 V. The
applied voltage is
(a)
30 V
(b)
50 V
(c)
40 V
(d)
150 V
In an ac circuit the power dissipated as heat is given by
(a)
VI
(b)
VI cos 
(c)
I 2R
(d)
V2/R
In an ac circuit the current :
(a)
is in phase with the voltage
(b)
leads the voltage
(c)
lags the voltage
(d)
any of the above depending on the circumstances
An ac is applied to resistive circuit. Which is true of the following?
(a)
Current leads in phase ahead of voltage
(b)
Current legs behind the voltage in phase
(c)
Current and voltage are in the same phase
(d)
Any of the above may be true depending upon the value of the resistance
In a circuit containing an inductance of zero resistance, the current lags behind the applied alternating voltage by a phase
angle :
(a)
90
(b)
45
(c)
30
(d)
0
When 100 V dc is applied across a solenoid, a current of 1A flows in it. When 100 V ac is applied across the same solenoid
the current drops to 0.5 A. If the frequency of the ac source is 50 Hz, the impedance and inductance of the solenoid are :
(a)
Q.23
Q.24
200  and 0.55 H
(b)
100  and 0.86 H
(c)
200  and 1.0 H
(d)
1100  and 0.93 H
An alternating voltage is connected in series with a resistance R and inductance L. If the potential drop across the resistance
is 200 V and across the inductance is 150 V, the applied voltage is :
(a)
350V
(b)
250V
(c)
500V
(d)
300V
An inductive circuit contains a resistance of 10 and an inductance of 2H. If an ac voltage of 120 V and frequency 60 Hz is
applied to this circuit, the current would be nearly :
(a)
0.72 A
(b)
0.16 A
(c)
0.48 A
(d)
0.80 A
26
Q.25
A 12 ohm resistor and 0.21 Henry inductor are connected in series to an ac source operating at 20 V, 50 cycle. The phase
angle between the current and the source voltage is :
(a)
Q.26
Q.27
Q.28
Q.29
Q.30
30
(b)
40
(c)
80
(d)
90
A coil having an inductance of 1/ henry is connected in series with a resistance of 300. If 20 volt from a 200 cycle source
are impressed across the combination, the value of the tangent of the phase angle between the voltage and the current is :
(a)
tan-1 5/4
(b)
tan-1 4/5
(c)
tan-1 3/4
(d)
tan-1 4/3
The power factor of series LCR circuit when at resonance is :
(a)
zero
(b)
0.5
(c)
one
(d)
depends on the values of L,C and R
The impendence of a circuit consists of 3 ohm resistance and 4 ohm reactance. The power factor of the circuit is :
(a)
0.4
(b)
0.6
(c)
0.8
(d)
1.0
In an ac circuit V and I are given by
V= 150 sin (150 t) V and
I = 150 sin (150 t + /3) A
The power dissipated in the circuit is
(a)
5625 W
(b)
4825 W
(c)
7450 W
(d)
3425 W
A resistor, an inductance and a capacitance are connected in series to an a.c supply. When measured with the help of an a.c.
voltmeter, the p.d. across the resistor is found to be 40 V, across the inductance 30 V, and across the capacitance 60 V. what
is the supply voltage ?
(a)
130 V
(b)
50V
(c)
70 V
(d)
100V
ANSWERSHEET
Induction & A.C.
1.
(b)
2.
(b)
3.
(b)
4.
(c)
5.
(b)
6.
(c)
7.
(b)
8.
(d)
9.
(c)
10.
(c)
11.
(a)
12.
(a)
13.
(c)
14.
(d)
15.
(c)
16.
(c)
17.
(b)
18.
(bc)
19.
(d)
20.
(c)
21.
(a)
22.
(a)
23.
(b)
24.
(b)
25.
(c)
26.
(d)
27.
(c)
28.
(b)
29.
(a)
30.
(b)
27
Electromagnetic Waves
1.
*2.
3.
*4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
A magnetic field can be produced only
(a)
a moving charge only
(b)
a changing electric field only
(c)
both of them
(d)
none of them
Choose the correct statement (s) :
The displacement current exists in the gap between the plates of a capacitor when the charge on the capacitor
(a)
is increasing with time
(b)
is decreasing with time
(c)
becomes constant
(d)
is zero
Electromagnetic waves are produced by :
(a)
a static charge
(b)
a uniformly moving charge
(c)
an accelerated charge
(d)
neutral particles.
Which of the following has/have zero average value in plane electromagnetic wave?
(a)
electric field
(b)
magnetic field
(c)
electric energy
(d)
magnetic energy
In a plane electromagnetic wave the phase difference between electric and magnetic field vectors is :
(a)
zero
(b)
/4
(c)
/2
(d)

An electromagnetic wave is passing through a small volume of space. The energy in the volume oscillates with
(a)
the frequency of the wave
(b)
double the frequency of the wave
(c)
half the frequency of the wave
(d)
zero frequency
Point out the wrong statement : Electromagnetic waves
(a)
are transverse
(b)
are produced by accelerating charges
(c)
electric energy
(d)
magnetic energy
The dimensions of 1/00 are :
(a)
LT-1
(b)
L-1T
(c)
L-2T2
(d)
L2T-2
The ratio of the amplitudes of electric and magnetic fields in an electromagnetic waves is
(a)
00
(b)
100
(c)
00
(d)
1/00
The amplitude of electric field in an electromagnetic waves is 5m-1. The amplitude of the magnetic field is :
(a)
5T
(b)
1.67 × 10-8 T (c)
1.5 × 109 T
(d)
1.67 × 10-10 T
A plane electromagnetic wave incident on a surface delivers momentum p and energy E. Then :
(a)
p  0, E  0
(b)
p = 0, E = 0
(c)
p  0, E = 0
(d)
p = 0, E  0
Select the correct statement :
(a)
Blue light has a higher momentum than red light
(b)
Red light has a higher momentum than blue light
(c)
Red light has an higher energy than blue light.
(d)
Blue light and red light have equal energies.
Heat radiations are :
(a)
-rays
(b)
microwaves
(c)
infrared radiations
(d)
radiowaves.
Chose the highest frequency waves :
(a)
ground waves
(b)
sky waves
(c)
television waves
(d)
visible light waves
Chose the electromagnetic radiation relevant to telecommunication :
(a)
ultraviolet
(b)
infrared
(c)
visible
(d)
microwave.
ANSWER SHEET
1.
(c)
2.
(a) (b)
3.
(c)
4.
(a) (b)
5.
(a)
6.
(b)
7.
(c)
8.
(d)
9.
(b)
10.
(b)
11.
(a)
12.
(a)
13.
(c)
14.
(d)
15.
(d)
28
OPTICS
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
An object is placed unsymmetrically between two plane mirrors such that a ray shooting form it is deviated
through 144 on successive reflections from the two mirrors. The total number of images seen in the two mirrors
is
(a)
5
(b)
4
(c)
2
(d)
infinite
A ray of light incident normally on face AB of an isosceles prism travels as shown in Fig. The least value of the
refractive index the prism must be
(a)
2
(b)
1.5
(c)
3
(d)
2.0
Light rays following at angle of incidence A ¾ on prism of angle A = 60, image with minimum divination given
by
(a)
90
(b)
60
(c)
45
(d)
30
Angle of prism is A and its one surface is silvered. Light rays falling at an angle of incidence 2A on the first
surface returns back through the same path after suffering reflection at the second silvered surface. The refractive
index of material of prism is
(a)
2 sin A
(b)
2 cos A
(c)
½ cos A
(d)
tan A
An angle of minimum deviation for a prism of refractive index 1.5 is equal to the angle of the prism. The angle of
the prism is
(a)
62
(b)
41
(c)
82
(d)
31
When a beam of light is allowed to fall normally on the longer side of an isosceles right angled prism with
refractive index greater than 2 , it emerges fro m the prism after having suffered a deviation. The angle of the
deviation is
(a)
180
(b)
> 90 but < 180
(c)
90
(d)
60
There is a prism with refractive index 2 and the refracting angle equal to 30. One of the refracting surfaces of
the prism is polished. A beam of monochromatic light will retrace its path if its angle of incidence over the
refracting surface of the prism is
(a)
0
(b)
30
(c)
45
(d)
60
A thin prism P1 with angle 4 and made from glass of refractive index 1.54 is combined with another thin prism P2
made from glass of refractive index 1.72 to produce dispersion without deviation. The angle of the prism P2 is
(a)
5.33
(b)
4
(c)
3
(d)
2.6
The power of a lens (n = 1.25) is 3D. When immersed in a liquid its power is -2D. The refractive index of the
liquid is
(a)
1.3
(b)
1.4
(c)
1.5
(d)
1.6
A convex lens of focal length  is cut into two indentical halves by a plane passing through a diameter and the
two pieces are placed symmetrically about the central axis with a small gap. A point source of light is placed on
the central line at a distance d such that d > . The two pieces will give rise to
(a)
no image
(b)
a single image of smaller intensity
(c)
two real images
(d)
two virtual images
The refractive index for flint glass for F line is 1.63327, for C line is 1.61611 and for D line is 1.62100. The
dispersive power of the flint glass between F and C lines is
(a)
0.02764
(b)
0.2764
(c)
2.764
(d)
27.64
The focal lengths of a thin convex lens are 100 cm and 96.8 cm for red and blue rays respectively. Calculate the
dispersive power of the material of lens
(a)
0.968
(b)
0.032
(c)
9.68
(d)
6.30
For making a direct vision spectroscope two prisms of crown glass each of angle 4 and one prism of flint glass
are used, If refractive indices of crown and flint glasses for yellow light are 1.515 and 1.655 respectively, the
angle of flint glass prism is
(a)
3.2
(b)
6.3
(c)
3.6
(d)
7.2
29
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
An astronomical telescope has an angular magnification of magnitude 5 for distant objects. The separation
between the objective and the eye-piece is 36 cm and the final image is formed at infinity. The focal length e of
the eye-piece are
(a)
0 = 45 cm, e = - 9 cm
(b)
0 = 50 cm, e = 10 cm
(c)
0 = 7.2 cm, e = 5 cm
(c)
0 = 30 cm, e = 6 cm
An achromatic combination is to be obtained using a convex and a concave lens. The two lenses chosen should
have
(a)
their powers equal
(b)
their refractive indicates equal
(c)
their dispersive powers equal
(d)
the product of their powers and dispersive powers equal
In an electromagnetic field, the amplitude of magnetic field is 3 10-10T. If the frequency of wave is 1012 Hz, the
amplitude of the associated em wave is
(a)
910-2 V/m
(b)
310-10 V/m
(c)
310-2 V/m
(d)
110-18 V/m
The optical path for  = 5890 A is the same it goes through 1.00cm of perspex or 1.14 cm of water. If the
refractive index of water is 4/3 the refractive index of perspex is
(a)
1.52
(b)
0.855
(c)
1.17
(d)
1.33
The width of one of the two slits in a young’s double slit experiment is double of the other slit. Assuming that the
amplitude of the light coming from a slit is proportional to the slit width, the ratio of the maximum to the
minimum intensity in the interfering pattern is
(a)
3
(b)
9
(c)
4
(d)
2
Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum
possible intensities in the resulting beam are
(a)
5I and I
(b)
5I and 3I
(c)
9I and I
(d)
9I and 3I
In the Young’s double slit experiment, the separation between the slit is halved and the distance between the slit
and screen is doubled. The fringe width is
(a)
unchanged
(b)
halved
(c)
doubled
(d)
quadrupled
In Young’s double slit experiment, if the slit width are in the ratio 1:9, the ratio of the intensity at minima to that
at maxima will be
(a)
1
(b)
1/9
(c)
1/4
(d)
1/3
The slits in a Young’s double slit experiment have equal width and a monochromatic source is placed
symmetrically with respect to the slits. The intensity at the zero order (central) fringe is I0. If one of the slits is
closed, the intensity at this point will be
(a)
I0
(b)
I0/4
(c)
I0/2
(d)
4I0
If Young’s double slit experiments is performed under water, then
(a)
the fringe width decreases
(b)
the fringe width increases
(c)
the fringe width remains unchanged
(d)
the fringes disappear
A thin mica sheet is placed in front of Young’s double slit so that both slits are cover
(a)
the fringe width decreases
(b)
the fringe width increase
(c)
the fringe width remains unchanged
(d)
the fringe system get displacement
In the Young’s double slit experiment, the interference pattern is found to have an intensity ratio between bright
and dark fringes as 9. This implies that
(a)
the intensities at the screen due to the two slits are 5 units and 4 units respectively
(b)
the intensities at the screen due to two slits are 4 units and 1 unit respectively
(c)
the amplitude ratio is 3
(d)
the amplitude ratio is 2
In Young’s double slit experiment a thin transparent sheet (n = 1.55) is placed directly behind one of the slits. The
thickness of the sheet is such that the optical path length of the light in the mica is 0.500m where m is the
wavelength of light in the sheet. The light used is 632.8nm. Then
(a)
the interference pattern is shifted by /2
(b)
the thickness of mica is 204nm
30
Q.27
Q.28
Q.29
Q.30
Q.31
Q.32
(c)
the dark fringe becomes bright and vice versa
(d)
the interference pattern disappears
In Young’s double slit experiment 52 fringes are obtained in the field of view with sodium light of  = 5893 A.
The number of fringes in the same field of view with mercury green light =5461A is
(a)
52
(b)
56
(c)
48
(d)
26
A thin film (n = 1.33) seen by light of wavelength 532nm appears dark by normal reflection. Its thickness is
(a)
200nm
(b)
100nm
(c)
400nm
(d)
266nm
White light falls normally upon a film of soapy water (n = 1.33) whose thickness is 5 10-5cm. If seen in reflected
light, it appears.
(a)
white
(b)
dark
(c)
green
(d)
red
Light of wavelength 4500A is found to be missing in the reflected light in a thin air film interference experiment
viewed normally. Thickness of the film is 6.7510-7m, then light of wavelength
(a)
5400A will also be missing in reflecting light
(b)
6750A will show a maximum in reflected light
(C)
5400A will be missing in the transmitted light
(d)
5400 A will show a maximum in the reflected light
A diffraction pattern is formed on a screen using red light. What happens if red light is reflected by green light?
(a)
no change
(b)
the central maximum becomes narrower and intense
(c)
the central maximum becomes broader and less intense
(d)
the central maximum becomes narrower and more intense
A beam of light of wavelength 600nm from a distant source falls on a single slit 1.00mm wide and the resulting
diffraction pattern is observed on a screen 2m away. The distance between the first dark fringe on either side of
the central bright fringe is
(a)
1.2 cm
(b)
1.2 mm
(c)
2.4cm
(d)
2.4 mm
ANSWER
OPTICS
1.
(a)
2.
(a)
3.
(d)
4.
(b)
5.
(c)
6.
(a)
7.
(c)
8.
(c)
9.
(c)
10.
(c)
11.
(a)
12.
(b)
13.
(b)
14.
(d)
15.
(d)
16.
(a)
17.
(a)
18.
(b)
19.
(c)
20.
(d)
21.
(c)
22.
(b)
23.
(a)
24.
(c)
25.
(b,d)
26.
(abc)
27.
(b)
28.
(a)
29.
(c)
30.
(d)
31.
(d)
32.
(d)
31
Modern Physics
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
For a slow moving electron, having kinetic energy E, the deBroglie wavelength is proportional to
(a)
E1/2
(b)
E
(c)
E-1/2
(d)
E-2
A photon of frequency v has a momentum associated with it. If c is the velocity of light, this momentum is
(a)
hv/c2
(b)
hv/c
(c)
v/c
(d)
h/c
The momentum of a photon and an electron are equal, then
(a)
both have equal energy
(b)
electron has more energy
(c)
photon has more energy
(d)
photon has no energy
The threshed wavelength for photoelectric emission from a material is 5200A. Photoelectrons will be emitted
when the material is illuminated with monochromatic radiation from
(a)
50 watt infrared lamp
(b)
1 watt infrared lamp
(c)
50 watt ultraviolet
(d)
1 watt ultraviolet lamp
A source of monochromatic light is placed at a distance of 1m from a photocell and cut off potential is found to be
V0. If the distance is doubled, The cut off potential will be
(a)
2V0
(b)
1.5V0
(c)
V0
(d)
0.5V0
A photocell is illuminated by a small bright source placed one metre away. When the same source is placed two
metre away, the electrons emitted by the photo cathode
(a)
each carries one quarter of its previous energy
(b)
each carries one quarter of its previous momenta
(c)
are half as numerous
(d)
are one quarter as numerous
In hydrogen spectrum H line arises due to transition of electron from n = 3 to n = 2. In the spectrum of singly
ionized helium there is a line having almost the same wavelength as that of H line. This is due to the transition
of electron between the states.
(a)
32
(b)
42
(c)
53
(d)
64
Atomic hydrogen is excited to the nth energy level. The maximum number of spectral lines which it can emit
while returning to the ground state is
(a)
½ n (n-1)
(b)
½ n (n+1)
(c)
n (n-1)
(d)
n (n+1)
The X-rays beam coming from an X-rays tube will be
(a)
monochromatic
(b)
having all wavelength smaller than a certain maximum wavelength
(c)
having all wavelength larger than a certain minimum wavelength
(d)
having all wavelength lying between a minimum and a maximum wavelength
The wavelength  of the X-rays line K of an anticathode element of atomic number Z is nearly proportional to
(a)
Z2
(b)
(Z-1)2
(c)
1/Z-1
(d)
1/ (Z-1)2
The wavelength of K line from an element of atomic number 41 is 1 then the wavelength of K line of an
element of atomic number 21 is
(a)
4
(b)
/4
(c)
3.08
(d)
0.26
The radius of a nucleus is
(a)
proportional to its mass number
(b)
inversely proportional to its mass number
(c)
proportional to the cube root of its mass number
(d)
not related to its mass number
The approximate density of nuclear matter is
(a)
105kg/m3
(b)
1010kg/m3
(c)
1015kg/m3
(d)
1020kg/m3
32
Q.14
Q.15
Q.16
Q.17
Q.18
Q.19
Q.20
Q.21
Q.22
Q.23
Q.24
The -, - and - rays emitted by a radioactive substance are passed through a region containing a magnetic field
at right angles to their path. Then
(a)
energy gained by -rays will be maximum
(b)
energy gained will be zero by all the three rays
(c)
momentum of rays will not change, while those -and -rays
(d)
momentum change will be zero for all the three days
The number of alpha particles emitted per minute by a small amount of substance was 480 initially and 240 after
2 hours. After another 4 hours the expected rate of emission per minute is
(a)
0
(b)
60
(c)
80
(d)
120
Consider a radioactive material of half-life 10 minutes. If one of the nuclei decays now, the next one will decay
(a)
after 1 minute
(b)
after 1 In 2 minute
(c)
after 1/N minutes, where N is the number of nuclei present at that moment
(d)
after any time
A radioactive material has half lives of 1620 years and 405 years for  and  emission respectively. The material
decays by simultaneous  and  emission. The time in which one-fouth of the material remains intact is
(a)
4675 years
(b)
720 years
(c)
648 years
(d)
324 years
The kinetic energy of a 300K thermal neutron is approximately
(a)
300eV
(b)
300keV
(c)
0.025eV
(d)
1.1MeV
235
Assuming that 200 MeV of energy is released per fission of 92 U nuclei, then the mass of 82235U consumed per
day in a fission reactor of power 1 megawatt will apprxoimately be
(a)
10-2g
(b)
1g
(c)
100g
(d)
1000g
The equation 411H24He + 2e + 2v + 26 MeV represents.
(a)
-decay
(b)
-decay
(c)
fusion
(d)
fission
2
4
The binding energy of deutron 1H is 1.112 MeV per nucleon and -particle 2He has a binding energy of 7.0471
MeV per nucleon. Then in the relation
2
2
4
1H + 1H 2He+ Q
the energy Q released is
(a)
1MeV
(b)
11.9MeV
(c)
23.8MeV
(d)
9.31MeV
With p for photon and n for neutron, the nuclear forces have strengths in the order of
(a)
p–p>p–p>n–n
(b)
n–n>p–n>p–p
(c)
n–n>p–p>p–n
(d)
n–n=p–p=p–n
The minimum energy of a -rays photons for pair production is nearly
(a)
1.1eV
(b)
1.1keV
(c)
1.1MeV
When do two protons attracts each other
(a)
the distance between them is 10-10m
(b)
the distance between them is 10-1m
(c)
the distance between them is 10-15m
(d)
this will never happen.
33
(d)
1.1BeV
Q.25
Q.26
Q.27
Q.28
Q.29
Q.30
Q.31
A proton and an electron are accelerated by same potential difference have de-Broglie wavelength p and e.
(a)
e = p
(b)
e < p
(c)
e > p
(d)
none of these.
An electron with initial kinetic energy of 100 eV is acceleration through a potential difference of 50 V. Now
the de-Broglie wavelength of electron becomes
(a)
1Å
(b)
1.5 Å
(c)
3 Å
(d)
12.27 Å.
Which of the following is correct?
(a)
Photoelectric current is proportional to applied voltage.
(b)
Increase in frequency of incident radiations results in the increase in the photocurrent.
(c)
Increases in applied voltage results in the increase in the photocurrent.
(d)
Increase in intensity of incident light results in the increase in photocurrent.
An electron microscope uses electrons accelerated by a voltage of 50 kV. The de-Broglie wavelength
associated with the electrons is
(a)
5.5  10-10 m (b)
5.5  10-11 m
(c)
5.5  10-12 m (d)
5.5  10-14 m
If de-Broglie wavelength associated with a neutron is 1.4 Å then K.E. of the neutron is (given mn = 1.675 
10-27 kg)
(a)
0.01 3 eV
(b)
0.049 eV
(c)
0.93 eV
(d)
0.042 eV
Light of wavelength 4000 Å is incident on barium. Photo electrons emitted describe a circle of radius 50 cm by
a magnetic field of flux density 5.26  10-6 Tesla. Work function of the barium is
(a)
3200 Å
(b)
3400 Å
(c)
3600 Å
(d)
3800 Å
If h is Planck is constant, m is mass of electron and C is velocity of light, then the dimension of h/mc is
(a)
[M0L0T]
(b)
[M0L0T0]
(c)
[M0LT0]
(d)
[ML0T0]
ANSWERSHEET
1.
(d)
2.
(c)
3.
(c)
4.
(c),(d)
5.
(c)
6.
(d)
7.
(d)
8.
(c)
9.
(c)
10.
(d)
11.
(a)
12.
(c)
13.
(c)
14.
(b)
15.
(b)
16.
(d)
17.
(c)
18.
(c)
19.
(b)
20.
(c)
21.
(c)
22.
(d)
23.
(c)
24.
(c)
25.
(c)
26.
(a)
27.
(d)
28.
(c)
29.
(d)
30.
(c)
31.
(b)
34
Semiconductor
Q.1
The output of amplifier-1 is the input for amplifier –2. If their gains are A1 and A2 respectively, the total gain of this twostage amplifier is
(a)
Q.2
Q.3
Q.4
Q.6
(b)
A1 - A2
(c)
A1  A2
(d)
A1 / A2
When donors are added to a semi-conducting material
(a)
number of electrons increases, number of holes remains unaltered
(b)
number of electrons increases, number of holes decreases
(c)
number of electrons decreases, number of holes increases
(d)
number of electrons remains unaltered, number of holes decreases
A piece of copper and another of germanium are cooled from room temperature to 80K. The resistance of
(a)
each of them increases
(b)
each of them decreases
(c)
copper increases and germanium decreases
(d)
copper decreases and germanium increases
The impurity atoms with which pure silicon should be doped to make a P-type semi-conductor are those of
(a)
Q.5
A1 + A2
phosphors
(b)
antimony
(c)
boron
(d)
aluminum
The concentration densities of electrons and holes in a N-type semi-conductor are n and p respectively. If this semiconductor is heated from temperature T to T’, then
(a)
p increases and n decreases
(b)
n increases and p decreases
(c)
both n and p increase, but always n>>p
(d)
both n and p increase, but n  p nI (T)
Read the following statements carefully :
Y : The resistivity of a semi-conductor decreases with increase of temperature
Z : In a conducting solid, the rate of collision between free electrons and ions increases with increase of temperature
Q.7
Q.8
Q.9
Q.10
(a)
Y is true but Z is false
(b)
Y is false but Z is true
(c)
Both Y and Z are true
(d)
Y is true and Z is the correct reason for Y
The depletion layer in a PN junction contains charges that are
(a)
Mostly majority carries
(b)
Mostly minority carries
(c)
Mobile donor and acceptor ions
(d)
Fixed donor and acceptor ions
When a forward bias is applied to a junction diode
(a)
Potential barrier increases
(b)
Potential barrier decreases
(c)
Majority- carrier current decreases to zero
(d)
Minority-carries current decreases to zero
The width of the depletion layer of a junction
(a)
decreases with light doping
(b)
increase with heavy doping
(c)
is independent of applied voltage
(d)
is increased under reverse bias
The turn-on voltage of a Ge junction diode is nearly
(a)
Q.11
0.7 V
(b)
0.3V
(c)
1.0V
In an unbiased PN-junction, the junction current at equilibrium is
(a)
due to diffusion of minority carries only
(b)
ue to diffusion of majority carries only
(c)
zero, because equal but opposite carries are crossing the junction
(d)
zero, because no charges are crossing the junction
35
(d)
0.1V
Q.12
A full wave rectifier is being used to rectify an alternative voltage of frequency 50Hz. The number of pulses of rectified
current obtained in one second is
(a)
Q.13
Q.14
Q.15
Q.16
Q.17
Q.18
Q.19
Q.20
Q.21
25
(b)
50
(c)
100
(d)
200
for transistor action
(a)
the collector must be more heavily doped than the emitter
(b)
the collector-base region must be reversed biased
(c)
the base region must be wide
(d)
the emitter must be N-type material
A transistor connected in CB configuration has
(a)
a low input resistance and a high output resistance
(b)
a high input resistance and a low output resistance
(c)
a low input resistance and a low output resistance
(d)
a high input resistance and a high output resistance.
When the emitter current of a transistor is charged by 1mA, its collector current changes by 0.995mA. Then
(a)
Common base gain  = 0.995
(b)
Common emitter gain = 199
(c)
Base current IB = 0.005mA
(d)
Reverse leakage currents ICEO and ICBO are related as ICEO = 200 ICBO
In an NPN transistor circuit, the collector current is 10mA. If 90% of the electors emitted reach the collector
(a)
the emitter current will be 9mA
(b)
the emitter current will be 11mA.
(c)
the base current will be 1mA.
(d)
the base current will be-1mA.
The condition which must be satisfied to operate the transistor in saturation mode is
(a)
the E / B and C / B junctions are forward biased
(b)
the E/B junction is forward biased and C/B junction is reverse biased
(c)
the E/B junction is reverse biased and C /B junction is forward biased
(c)
the E /B and C /B junctions are reverse biased
A transistor is used in common emitter mode as an amplifier. Then
(a)
the base-emitter junction is forward biased
(b)
the base-emitter junction is reverse biased
(c)
the input signal is connected in series with the voltage applied to the base-emitter junction
(d)
the input signal is connected in series with the voltage applied to bias the base-collector junction.
n the middle of the depletion layer of a reverse-biased p-n junction, the
(a)
electric field is zero
(b)
potential is maximum
(b)
electric field is maximum
(d)
potential is zero
For a transistor amplifier, the voltage gain
(a)
remains constant for all frequencies
(b)
is high at high and low frequencies and constant in the middle frequency range
(c)
is low at high and low frequencies and constant at mid frequencies
(d)
none of the above
When npn transistor is used as an amplifier
(a)
electrons move from base to collector
(b)
holes move from emitter to base
(c)
electrons more from collector to base
(d)
holes move from base to emitter.
36
Semiconductor Physics
1.
(c)
2.
(b)
3.
(d)
4.
(c), (d)
5.
(d)
6.
(c)
7.
(d)
8.
(b)
9.
(d)
10.
(b)
11.
(c)
12.
(c)
13.
(b)
14.
(a)
15.
(a), (b)
16.
(b), (c)
17.
(a)
18.
(a), (c)
19.
(a)
20.
(c)
21.
(a)
37