59.
A ball of mass m approaches a wall of mass
normal to the wall. The speed of wall is 1 m/s
after an elastic collision with the wall is
(a) 5 m/s away from the wall
(c) 3 m/s away from the wall
M (>>m) with speed 4 m/s along the
towards the ball. The speed of the ball
(b) 9 m/s away from the wall
(d) 6 m/s away from the wall
Sol.: Let v be the velocity of ball after collision, collision is elastic
 e=1
by relative velocity of separation = relative velocity of approach
 v –1 = 4 + 1 or v = 6 m/s
(away from the wall)

(d)
M
60.
A gun fires a shell and recoils horizontally. If the shell travels along the barrel with
speed v, the ratio of speeds with which the gun recoils, if the barrel is (i) horizontal (ii)
inclined at an angle of 300 with horizontal, is
(a) 1
Sol.:
(b)
2
(c)
3
mv  Mv1
mv
 v1 
M
mv cos 30 0  Mv 2
 v2 
(d)
1
2
… (i)
3mv
2M
… (ii)
From equation (i) and (ii) we get,

3
2
v1
2

v2
3
(b)
M
61.
A glass marble dropped from a certain height above the horizontal surface reaches the surface
in time t and then continues to bounce up and down. The time in which the marble finally
comes to rest is (coefficient of restitution is e)
(a)
Sol.:
e nt
(b)
Let height be h, so t 
and
v  2 gh  gt
Now
T t 
e 2t
2h
g
2ev 2e 2 v

 .......
g
g
(c)
1  e 
t
1  e 
(d)
1  e 
t
1  e 

t 
2ev
(1  e  e 2  ...)
g
t 
2 gt  e   1  e 

  t

g 1  e  1  e 
(c)
M
52.
A projectile is fired from the surface of earth of radius R with a velocity kve where ve is the
escape velocity and k  1. Neglecting air resistance, the maximum height of rise will be
(a)
Sol.:
R
2
k 1
(c)
(b)
2
k R
(c)
k 2R
1 k 2
kR
(d)
By conservation of energy,
1 2
mgh
mv 
h
2

1  
 R
r
h
R
v  kve  k 2 gR
1
mg h
m(k 2 gR ) 2 

2
1 h / R
2
k R
h
1 k 2
here
M
53.
If we assume only gravitational attraction between proton (mass M) and electron (mass m)
in a hydrogen atom and also assume Bohr’s quantization condition, then the expression for
the nth orbit energy of the H-atom will be
2

GMm
(a) 
2 2 mGMm
(b) 
n2h2
n2h2
2 2 GMm
(c) 
n2h2
Sol.:
T .E 
 GMm
2r
2
2
(d) none of the above
Also,
GMm 2
mv 2 GMm
GMm GMm2

 2  r

P

r
r
r
mv 2
P2
n2h2
nh
nh
2
 GMm r 
r 
mvr 
2
2
4 2 GMm 2


 2 2 mGMm 
T .E 
n2h2
2
(b)
M
54.
An artificial satellite of mass m is moving in a circular orbit at a height h equal to
radius of the earth from the earth’s surface. Suddenly due to internal explosion the
satellite breaks into two parts of equal masses. One part of the satellite stops just after
the explosion and then falls to the surface of the earth. The increase in mechanical
energy of the system (satellite + earth) due to explosion will be (acceleration due to
gravity on the earth’s surface is g)
(a) mgR
Sol.:
(b) mgR/2
Applying conservation of momentum mv 
(c) mgR/4
(d) 3mgR/4
m
m
 0  v'  v'  2v
2
2
Increase in mechanical energy of the system 
1m
2v 2  1 mv 2  1 mv 2  GMm
2 2
2
2
2  2 R 
mgR 2 mgR


4R
4

(c)
M
71.
A particle is moving with a constant angular acceleration of 4 rad/s2 in a circular path. At
t = 0, particle was at rest. Find the time at which the magnitudes of centripetal acceleration
and tangential acceleration are equal.
(a) 1 s
Sol.:
(b) 2 s
(c)
1
s
2
(d)
1
s
4
at = 4R
aN = 2R = (t)2R
at = aN 16 t2 = 4, t =

1
s
2
(c)
M
72.
Two blocks of masses 4 kg and 2 kg are connected by a
heavy string of mass 3 kg and placed on rough horizontal
plane. The 2 kg block is pulled with a constant force F as
shown in figure. The coefficient of friction between the
bocks and the ground is 0.5. What is the value of F so that
tension in the string is constant throughout during the
motion of the blocks.
4kg
2kg
F
(a) 40 N
(b) 30 N
Sol.: For a = 0, tension is constant throughout
F    (4  2  3)  g  0.5  9  10  45 N

(c)
(c) 45 N
(d) 60 N
M
73.
Two persons are holding a massless rope tightly at its ends so that it is horizontal. A 15 kg
weight is attached to the mid point of the rope, which now no longer remains horizontal.
The minimum tension required to completely straighten the rope is
(a) 15 kg
Sol.:
(b)
15/2 kg
2T sin   mg
mg
 T 
2 sin 
(c) 5 kg
(d) infinitely large
2T sin 
T

T cos 
But   0
 T 

(d)
T

T cos 
mg
M
74.
A string of length L and mass M is lying on a horizontal table. A force F is applied at one end
of string. Tension in the string at a distance x from the end at which force is applied is
(a) zero
(b) F
F T 
Sol.: (c)
(c) F(L – x)/L
M
xa
L
lx
T
(d) F(L – x)/M
T
x
F
M
( L  x)a
L
F

T  ( L  x)
L
T
52.
The bulk modulus of rubber is 9.8  108 N/m2. To what depth a rubber ball be taken in a lake
so that its volume is decreased by 0.1%?
(a) 25 m
Sol.:
B
(b) 100 m
P
or
V / V
P   B.

 0. 1 
P  9.8  10 8  

 100 
or
 0.1 
hg  9.8  108  

 100 

h

(b)
(c) 200 m
(d) 500 m
V
V
9.8  108 0.1
m = 100 m

1000  9.8 100
E
53.
A cylindrical tank has a hole of 1 cm2 in its bottom. If the water is allowed to flow into the
tank from a tube above it at the rate of 70 cm3/sec then the maximum height up to which
water can rise in the tank is
(a) 2.5 cm
(b) 5 cm
(c) 10 cm
(d) 0.25 cm
Sol.:
The height of water in the tank becomes maximum when the volume of water flowing into
the tank per second becomes equal to the volume flowing out per sec. Volume of water
flowing out per second
 Av  A 2 gh
Volume of water flowing in one second = 70 cm3/sec
A 2 gh  70,

h  2.5 cm

(a)
1  2 gh  70 or
2  980  h  4900
E
54. A cylindrical vessel contains a liquid of density  upto a
height h. The liquid is closed by a piston of mass m and
area of cross-section A. There is a small hole at the bottom
of the vessel. The speed v with which the liquid comes out
of the hole is: (neglect presence of atmosphere)
2 gh
(a)
(b)
2 gh 

mg 

2 gh 
A 

(c)

v
mg 

2 gh 

A 

(d)
mg
A
Sol.: Applying Bernoulli’s theorem at 1 and 2
mg 1 2
gh 
 v
A 2
or
m, A
h
m, A
h

mg 

v  2 gh 
A 

(b)
1
2
v
E
72.
A cylinder vessel of diameter 0.3m, height 0.6m, is filled two-thirds with liquid of specific
gravity 0.8. The vessel is rotated about its axis. Find the angular velocity of the vessel when the
base is just visible. (g = 10 m/s2)
(a) 16.2 rad/s
Sol.:
ymax  ymin
(b) 23.1 rad/s
2 R 2

2g
y max  0.6, y min  0    23.1 rad/s

(d)
(c) 12 rad/s
(d) 10 rad/s
M
73.
Drops of liquid of density d are floating half immersed in a liquid of density . If the surface
tension of liquid is T, then radius of the drop will be
 3T



 g ( 2 d  ) 
(a)
Sol.:
(b)
 3T 


 g (d  ) 
(c)
 6T



 g (2d  ) 
(d)
 6T 


 g (d  ) 
For equilibrium of drop
2 3
4
R g  2RT  R 3 dg
3
3
2 RT 
2 3
R g 2d   
3
3T
2d  g
R

(a)
M
74.
A solid sphere of radius R made of a material of Bulk modulus K is surrounded by a liquid in a
cylindrical container. A light piston of area A floats on the surface of the liquid. When a mass
m is placed on the piston to compress the liquid, the fractional change in the radius of the
sphere will be
(a)
Sol.:
mg
AK
(b)
3mg
AK
(c)
By definition, Bulk’s modulus K  
V 
4 3 dV
dR
R 
3
, K
3
V
R

mg
3 AK
(d)
mg
2 AK
dP
mg
=
dV / V
 dV 


V 
mg
dR
mg


R
3 AK
 dR 
3 A 
 R 
(c)
M
75.
A material has Poisson’s ratio 0.5. If a uniform rod of it suffers a longitudinal strain of
2 × 10–3, what is the percentage increase in volume?
(a) 2 %
(b) 4 %
(c) 0 %
(d) 5 %
Sol.:
V (r 2 L) L
r


 2
2
V
L
r
r L

(r / r )
(L / L)
or
r
L
 
 1  10 3
r
L

V
= 2 10 3  2 10 3 = 0
V

(c)
M
74.
An insect of negligible mass is sitting on a block of mass
M, tied with a spring of force constant k. The block
performs simple harmonic motion with amplitude
Ainfront of a plane mirror placed as shown. The maximum
speed of insect relative to its image will be
(a) A
Sol.:
k
M
(b)
A 3
2
k
M
(c) A 3
The maximum velocity of the insect is A

(c)
k
M
k
.
M
Its component perpendicular to the mirror is A
Thus maximum relative speed  3 A
600
k
.
M
k
sin 600.
M
(d)
A k
2 M
M
M
76.
In the diagram shown, the object is performing SHM
according to the equation y  2 A sin( t ) and the
plane mirror is performing SHM according to the


equation Y   A sin  t   . The diagram shows
3

the state of the object and the mirror at time t = 0 sec.
The minimum time from t = 0 sec after which the
velocity of the image becomes equal to zero?

3
(b)
3

Velocity of image = v0  2vm = 0
(a)
Sol.:


2 A cos t  2 A cos t  
3


(d)
(c)

t=
Plane Mirror
y
Object

6
(d)
2
3
2
3
M
77.
In a converging lens of focal length f and the distance
between real object and its real image is 4f. If the object
f
x1
moves x1 distance towards lens its image moves x2
distance away from the lens and when object moves y1
x2
y1 O
y2 I
4f
distance away from the lens its image moves y2 distance
towards the lens, then choose the correct option
Sol.:
(a)
x1  x2 and y1  y2
(b)
x1  x2 and y1  y2
(c)
x1  x2 and y1  y2
(d)
x1  x2 and y2  y1
When distance between real object and its real image is 4f for a converging lens, both object
and its image are at a distance of 2f from the lens.

(c)
M
M
M
80.
A ray of light enters into a transparent liquid from air as
shown in the figure. The refractive index of the liquid
varies with depth x from the topmost surface as
1
x where x in meters. The depth of the
 2 
2
liquid medium is sufficiently large. The maximum
450
air
depth reached by the ray inside the liquid is
1
(a) 2 m
(b)
(c) 0.5 m
m
2
1.
(d) 1 m
If the temperature of the sun is increased from T to 2T and its radius from R to 2R, then the
ratio of the radiant energy received on earth to what it was previously will be
(a) 4
(b) 16
(c) 32
(d) 64
P  AT 4 and A  r 2
Sol.:

Now,
P  r 2T 4
T   2T , r  2r
Hence, P  4 16P  64P

(d)
E
2.
A steel tape gives correct measurement at 20°C. A piece of wood is being measured with the
steel tape at 0°C. The reading is 25 cm on the tape. The real length of the given piece of
wood must be
(a) 25 cm
Sol.:
(b) less than 25cm
(c) more than 25 cm
(d) none of these
On heating the distance between the divisions increase and hence it measures less than
actual value. But when temperature decreases, distance between divisions decreases and it
measures more than actual value.

(b)
E
3.
Heat required to melt 1 gm of ice is 80 cal. A man melts 60 gms of ice by chewing it in 1
minute. His power is
(a) 4800 W
Sol.:
P

(b) 336 W
(c) 80 W
(d) 0.75 W
Q mL 60  80  4.2


= 336 W
t
t
60
(b)
E
4.
The temperature of cold junction of a thermocouple is –20°C and the temperature of
inversion is 560°C. The neutral temperature is
(a) 270°C
Sol.:
(b) 560°C
θ θ
560  20
θn  i c 
 270C
2
2

(a)
(c) 1120°C
(d) 290°C
E
5.
Two litres of water at initial temperature of 27°C is heated by a heater of power 1 kW in a
kettle. If the lid of the kettle is open, then heat energy is lost at a constant rate of 160 J/s. The
time in which the temperature will rise from 27°C to 77°C is (specific heat of water
= 4.2 kJ/kg)
(a) 5 min. 20 sec.
50 sec.
Sol.:
(b) 8 min. 20 sec.
Heat gained by water = Heat supplied – Heat loss
ms  1000t 160t 

E
(c) 10 min. 40 sec.
(b)
t
2  4200  50
 8 min .20 sec .
840
(d) 12
min.
Sol.:
At maximum depth the ray graze the surface (i.e. the angle made by the ray with
normal will become 900)
1 

Applying Snell’s law 1 sin 450   2 
x  sin 90 0
2 

1
1

or x = 1 m
2
x
2
2

(d)
M
80.
A solid sphere of mass M is attached to two massless
springs each of spring constant k. It can roll without
slipping along a horizontal surface. If the system is
released after a small stretch in spring, then the time
period of oscillations will be :
7M
7M
7M
(a) 2
(b) 2
(c) 
2k
5k
10k
(d) 2
M
k
Sol.:
1
1
2k (2 R) 2  I2  constant
2
2
7
4kR2  2  MR 2 2  constant
10
d 7
d
 MR 2 2
0
dt 10
dt
(c)
 T 
4kR2 2

D
81.
Sol.:
7M
10k
A thin rod of mass m and length l is hinged at a point
which is at a distance h (h<l) above the horizontal
surface. The rod is released from rest from the
horizontal position. If e is the co-efficient of
restitution, the angular velocity of rod just after
collision will be (h = 1m, l = 2m, e = 1)
3 3g
6 3g
5 3g
(a)
(b)
(c)
8
8
8
mgl
1
sin   I2
2
2
3

g
4
Component of v along line of impact =
v cos 
l
h
(d) none of these


vcos


v
vcos
Before collision
After collision
v cos 2 
Angular velocity after collision =
=  cos 2 
l

(a)
D
82.
A disc of mass m and radius R is lying on a smooth horizontal surface. A
particle of mass m moving horizontally with a velocity v0 , collides with
the disc at B and sticks to it. Speed of the point A on the disc just after
impact will be
(a)
(c)
Sol.:
31
v0
8
5v0
16
(b)
5
v0
16
(d)
v0
2




 R2 1
R
mR 2  


sin 30º (kˆ)   m
 mR 2 
2
4
2
4



COM, mv0 iˆ  2mvcm  vcm 
COAM about CM  mv0
v0 ˆ
i
2
m v0
R/2
A
B
 v
  0 ( kˆ)
4R
 


vA  vcm    r
A
m v0 B
 cm v
R/2
cm

R 3
v0 ˆ v0
3R
i
(kˆ)   .
iˆ 
2
4R
4
2 2

11v0 ˆ
3v0 ˆ
i
j
16
16

ˆj 



31
| v A |
v0
8

(a)
D
39.
Speed of sound wave is v. If a reflector moves towards a stationary source emitting waves of
frequency f with speed u, the frequency of reflected wave will be
(a)
Sol.:
vu
vu
f (b)
f
vu
v
(c)
Apparent frequency for reflector would be
vu
f
vu
(d)
vu
f
v
vu
f1  
f
 v 
After being reflected the apparent frequency will further change and the reflector will now
behave as a source. The apparent frequency will now become :
 v 
f2  
 f1
vu
vu
f
vu
Finally we get f 2  

(c)
M
40.
The intensity of sound after passing through a slab decreases by 20%. On passing through
two such slabs, the intensity will decrease by
(a) 50 %
(b) 40 %
(c) 36 %
(d) 30%
Sol.:
Intensity after passing through first slab = 80% of I 0  0.8I 0
Intensity after passing through second slab = 80% of 0.8 I0 = 0.64 I0
Decrease in intensity  I 0  0.64 I 0  0.36 I 0

(c)
M
41.
The length of a sonometer wire AB is 110 cm. Where should the two bridges be placed from
A to divide the wire in three segments whose fundamental frequencies are in the ratio of
1:2:3?
(a) 30 cm, 90 cm
Sol.:
(b) 60 cm, 90 cm
(c) 40 cm, 70 cm
(d) None of these
As n1 : n2 : n3  1 : 2 : 3

1 1 1
l1 : l 2 : l3  : :  6 : 3 : 2
1 2 3

l1 

bridges should be placed from A at 60 cm and 90 cm.

(b)
110
110
 6  60 cm ; l 2 
 3  30 cm
11
11
M
42.
Sol.:
A sound wave of wavelength  travels towards the right horizontally with a velocity V. It
strikes and reflects from a vertical plane surface, traveling at a speed v towards the left. The
number of positive crests striking in a time interval of three seconds on the wall is
(a) 3(V  v) / 
(b) 3(V  v) / 
(c) (V  v) / 3
(d) (V  v) / 3
The relative velocity of sound waves with respect to the walls is V  v.
Hence, the apparent frequency of the waves striking the surface of the wall is
The number of positive crests striking per second is the same as frequency.
In three seconds, the number is [3(V  v)] / .

(a)
(V  v)
.

75.
In Young’s double slit experiment,double slit of separation 0.1 cm is illuminated by white
light. A coloured interference pattern is formed on a screen 100 cm away. If a pin hole is
located on this screen at a distance of 2 mm from the central fringe, the wavelength in the
visible spectrum which will be absent in the light transmitted through the pin-hole are
(a) 5714 Å and 4444 Å (b) 6000 Å and 5000 Å
(c) 5500 Å and 4500 Å (d) 5200 Å and 4200 Å
Sol.:
Absent wavelengths correspond to interference minima

y

2 yd
40000

d sin   2n  1  d  2n  1   

2
D
2
D2n  1 2n  1
 13333 Å , 80000 Å, 5714 Å, 4444 Å, 3636 Å

78.
(a)
A thin film of thickness t and index of refraction 1.33 coats a glass with index of refraction
1.50. Which of the following thickness t will not reflect normally incident light with
wavelength 640 nm in air?
(a) 120 nm
Sol.:
(b) 240 nm

21t  (2n  1) , t 
2

(2n  1)
21
(c) 300 nm
(d) 480 nm

2 t = 120 nm, 360 nm, .....
(a)
M
79.
Sol.:
3
is placed near one the slits in
2
Young’s double slits experiment, the intensity at the centre of the screen reduces to
half of the maximum intensity. The minimum thickness of the sheet should be




(a)
(b)
(c)
(d)
4
8
2
3


I  4 I 0 cos 2  2 I 0  4 I 0 cos 2
2
2
When a thin transparent sheet of refractive index  

1

2
2

cos

  2
 

4 2
Path difference x 

  1t  
4

  


2
2 2 4
or 0.5t 


 t min 
4
2

(c)
1.
The displacement-time graph of particle is shown in figure.
Choose the correct alternative.
(a) Work done by all the forces in part OA is greater than
zero
(b) Work done by all the forces in part AB is greater than
zero
(c) Work done by all the forces of in part BC is greater than
zero.
(d) Work done by all the forces of in part AB is less than zero
Sol.: Work done is positive when slope of the graph increases.
 (b)
S
C
A
B
t
O
E
2.
A small block of mass 0.1 kg is pressed against a horizontal
spring fixed at one end to compress the spring through 5.0 cm
as
shown.
The
spring
constant
is
100 N/m. When released the block moves horizontally till it
leaves the spring. It will hit the ground 2 m below the spring.
(a) at a horizontal distance of 1 m from free end of the
spring
Y
m = 0.1 kg
2m
X
O
(b) at a horizontal distance of 2 m from free end of the spring
(c)
vertically below the edge on which the mass is resting
(d) at a horizontal distance of
2 m from free end of the spring.
2
1
1
 5 
2
(100)
  mv  v 
2
100
2


Sol.:

2h
5
; xv
 1m
g
2
(a)
E
3.
A particle is acted upon by a force of constant magnitude which is always perpendicular to the
velocity of the particle. The motion of the particle takes place in a plane. It follows that
(a) its velocity is constant
(c)
(b)
its kinetic energy is constant
Sol.:
its acceleration is constant
(d) it moves in a straight line
(c)
E
4.
Two identical balls are projected, one vertically up and the other at an angle of 30° with the
horizontal, with same initial speed. The potential energy at the highest point is in the ratio
(a) 4 : 3
(b) 3 : 4
(c) 4 : 1
(d) 1 : 4
Sol.:
h1 
u2
(u sin 30) 2 u 2
, h2 

2g
2g
8g
h1 : h2  4 : 1

3.
(c)
A capacitor of capacitance ‘C’ is connected with a battery of emf ε
as shown. After full charging a dielectric of same size of capacitor
and dielectric constant k is inserted then choose correct statements.
(capacitor is always connected to battery)
C

(a) electric field between plates of capacitor remain same
(b) charge on capacitor is Cε
(c) energy on capacitor decreased
(d) electric field between plates of capacitor increased.
Sol.:
P.D. same and electric field same

(a)
E
4.
Shown in the figure is a distribution of charges. The flux of
electric field due to these charges through the surface is
(a) 3 q / 0
(b) 2 q / 0
(c) q / 0
(d) zero
–q
+q
–q
Sol.:
(d)
E
5.
Two spherical conductors A and B of radii 1 mm and 2 mm are separated by a distance of
5 cm and are uniformly charged. If the spheres are connected by a conducting wire then in
equilibrium condition, the ratio of the magnitude of the electric fields at the surface of
spheres A and B is
(a) 1 : 4
Sol.:
E A rB 2


E B rA 1

E
(b) 4 : 1
(d)
(c) 1 : 2
(d) 2 : 1
6.
A point charge + q is fixed at point B. Another point charge + q
at A of mass m vertically above B at height h is dropped from
rest. Choose the correct statement
(a) It will collide with B
(b) It will execute S.H.M
+q A
q2
(c) It will go down only if
< mgh2
40
+q B
h
(d) go down up to a point and then come up.
Sol.:
For charge + q at A to come down, Fe < mg

q2
 mg
40 h 2

(c)
E
7.
The electric field intensity at a point at a distance 2 m from a charge q is E. The amount of
work done in bringing a charge of 2 coulomb from infinity to this point will be
(a) 2E joules
Sol.:
(b) 4E joules
Potential at this point, V 
(c)
E
joules
2
(d)
E
joules
4
q
 rE  2 E
40 r
Work done = qV = 4E joules.

6.
(b)
A heater coil is cut into two equal parts and only one part is now used in the heater. The heat
generated will now be (Assuming potential difference is same in both cases)
(a) one fourth
times
Sol.:
H
(b) halved
1
R
R becomes half so heat generate will be doubled.

E
(c)
(c) doubled
(d) four
7.
In the circuit shown the potential difference between points
C and B will be
(a) (8/9) volt
(b) (4/3) volt
(c) (2/3) volt
(d) 4 volt
C 5
5
5
A
+ –
2V
5 B
5
5
D
Sol.:
I
V
2
 A (I is current in each branch)
Re 15
VC  VB 

4
V
3
(b)
E
8.
The current through 2  resistor is
(a) zero
(b) 1 amp
(c) 2 amp
(d) 4 amp
10V
5 10
20V
2
Sol.:
(a)
E
9.
The equivalent resistance between points A and B in
the circuit shown is
(a) 4 
(b) 6 
(c) 10 
(d) 8 
A
4
6
B
8
8
8
4
4
2.


A homogeneous electric field E and a uniform magnetic field B are pointing in the same

direction. A proton is projected with its velocity parallel to E. It will
(a) Go on moving in the same direction with increasing velocity
(b) Go on moving in the same direction with constant velocity
(c) Turn to its right
(d) Turn to its left
Sol.:
Here magnetic force is zero, but the velocity increases due to electric force.

E
(a)
3.
Three identical bar magnets each of magnetic moment M, are
placed in the form of an equilateral triangle with north pole
of one touching the south pole of the other as shown. The net
magnetic moment of the system is
(a) zero
(b) 3 M
(c)
3M
2
(d)
M 3
N S
N
S
N
Sol.:
Magnetic moment vectors of three bar magnets represent three side of a triangle taken in
order.

(a)
E
4.
Which of the following is true?
(a) Diamagnetism is temperature dependent
(b) Paramagnetism is temperature dependent
(c) Paramagnetism is temperature independent
(d) None of the above
Sol.:
E
S
(b)
5.
The magnetic induction field at the centre C of the arrangement shown in figure is
(a)
 0i
(1  )
4r
 i
(c) 0 (1  )
r
Sol.:
B
(b)
 0i
(1  )
2r
P
S
C
 i
(d) 0 (1  )
r
r
Q
0 I 0 I 0 I


(1  )
4r 4r 4r

(a)
E
2.
Two circular coils P and Q are arranged coaxially as shown,
and the sign convention adopted that currents are taken as
positive when flow in the direction of the arrows
P
Q
(a) If P carries a steady positive current and P is moved towards Q, a positive current is
induced in Q
(b) If P carries a steady positive current and Q is moved towards P, a negative current is
induced in Q
(c) If a positive current flowing in P is switched off a negative current is induced momentarily
in Q
(d) If both coils carry positive currents, the coils repel one another
Sol.:
(b)
E
3.
The two coils of self-inductance 4 H and 16 H are wound on the same iron core. The
coefficient of mutual inductance for them will be
(a) 8 H
Sol.:
(b) 10 H
(c) 20 H
(d) 64 H
M  K L1 L2
Here,
K=1

M  4  16  8 H

(a)
E
4.
Two pure inductors, each of self inductance L are connected in parallel but are well
separated from each other, then the total inductance is
(a) L
Sol.:
(b) 2 L
(c)
(c) L / 2
(d) L / 4
2.
A solenoid has an inductance of 10 henry and a resistance of 2. It is connected to a 10 V
battery. Time it takes for the magnetic energy to reach (1/4)th of its maximum value is
approximately
(a) 2s
(b) 3s
(c) 3.5s
(d) 2.5 s
2
Sol.:
tR

 
1
1 1
Given, L I 02 1  e L    LI 02
2
4 2



1  e   14  t ~ 3.5s

(c)
t / 5 2
E
3.
A capacitor is charged to a potential of V0. It is
connected with an inductor through a switch S. The
switch is closed at time t = 0. Which of the following
statement is correct.
(a) maximum current in the circuit is V0
LC
(b) potential across capacitor becomes zero for the
first time at t =  LC
(c)
energy stored in the inductor at time

LC is
2
1
CV02
4
(d) maximum energy stored in the inductor is
1
CV02 .
2
+ –
L
C
S
Sol.:
Imax = Q. = C.V.
1
LC
maximum energy stored =

C
L
 V0
1 2
1
LI max  CV02
2
2
(d)
E
4.
A L-C circuit (inductance 0.01 H, capacity 1F) is connected to a variable frequency ac
source. If frequency varies from 1 kHz to 2 kHz, then frequency at which the current in LC
circuit is zero is at
(a) 1.2 kHz
Sol.:
(b) 1.4 kHz
(c) 1.6 kHz
(d) 1.8 kHz
Resonance frequency,
f=
1
2 LC


1
2 0.0110 6

10 4
1.6 kHz
2
(c)
E
5.
A capacitor and resistor are connected with an A.C. source as
shown in figure. Reactance of capacitor is XC = 3 and resistance
of resistor is 4 . Phase difference between current I and I1 is
XC =3
 1  4 

 tan  3   53º 
 


R=4
I1
I
~
V=V0 sin t
Sol.:
(a) 
(b) zero
Using method of phasors,
tan  
(c) 53º
(d) 37º
IC
IC 4

I1 3
I
 = 530
so phase difference between I and I1 is 530

(c)

V ,IR=I1
E
3.
The probability of a radioactive atom for not disintegrating till 3 times of its half life is
(a) 1/3
(b)1/4
(c) 1/8
(d) 7/8
Sol.:
Probability = (not disintegrate for 1st half) × (not disintegrate in 2nd half) × (not disintegrated
in 3rd half = ½ x ½ x ½ =

1
8
(c)
E
4.
The time by a photoelectron to come out after the photon strikes is approximately
(a) 101s
Sol.:
1010 sec.

(c)
(b) 104s
(c) 1010s
(d) 1016s
E
5.
The wavelength of a certain line in the x-ray spectrum for tungsten (Z = 74) is 200 Å. What
would be the wavelength of the same line for platinum (Z = 78)? The screening constant a is
unity.
(a) 179.76 Å
Sol.:
(b) 189.76 Å
(c) 289.76 Å
(d) 379.76 Å
Using Moseley’s law, we get
 2 ( Z1  a) 2

1 ( Z 2  a) 2
2 

200  (74  1) 2
 179.76 Å
(78  1) 2
(a)
E
6.
Sol.:
When 3Li7 nuclei are bombarded by protons, and the resultant nuclei are 4Be8, the emitted
particles will be
(a) neutrons
(b) alpha particles
(c) beta particles
(d) gamma photons
Gamma-photon

(d)