1. OBJECTIVE LEVEL - I
1. If the KE of a body becomes four times of its initial value, then the new momentum will be :
(a) three times its initial value (b) four times its initial value
(c) twice its initial value (d) unchanged.
2. A shell explodes and many pieces fly off in different directions. The following is conserved :
(a) Kinetic energy (b) Momentum
(c) Neither momentum nor KE (d) Momentum and KE.
3. Which one of the following statement is true :
(a) Momentum is conserved in elastic collisions but not in inelastic collision
(b) Total KE is conserved in elastic collisions but momentum is not
(c) Total KE is not conserved but momentum is conserved in inelastic collision
(d) KE and momentum both are conserve in all types of collisions.
4. A bag of mass M hangs by a long thread and a bullet (mass m) comes horizontally with velocity v and
gets caught in the bag. Then for the combined system (bag + bullet) :
(a) Momentum is mMv/(M+m) (b) KE is (1/2)Mu2
(c) Momentum is mv(M+m) /M (d) KE m2
v2
/2(M+m).
5. A mass m1
moves with a large velocity. It strikes another mass m2
at rest in a head on collision. It
comes back along its path with losser speed after collision. Then :
(a) m1
> m2
(b) m1
< m2
(c) m1
= m2
(d) there is no relation between m1
and m2
.
6. Choose incorrect one. If no external force acts on a system :
(a) Velocity of centre of mass remains constant
(b) Velocity of centre of mass is not constant
(c) Velocity of centre of mass may be zero
(d) Acceleration of centre of mass is zero.
7. Two particle A and B initially at rest, move towards each other under a mutual force speed of A is V
and the speed of B is 2V, the speed of the centre of mass of the system is :
(a) zero (b) V
(c) 1.5V (d) 3V.
8. A ball of mass m moving with a speed u undergoes a head-on elastic collision with a ball of mass nm
initially at rest. The fraction of the incident energy transferred to the heavier ball is
(a)
n
1 n

(b) 2
n
(1 n)

(c) 2
2n
(1 n)

(d) 2
4n
(1 n)

.

2. 9. Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on a
frictionless horizontal surface. An impulse gives a velocity of 14 ms-1
to the heavier block in the
direction of the lighter block. The velocity of the centre of mass is :
(a) 30 ms-1
(b) 20 ms-1
(c) 10 ms-1
(d) 5 ms-1
.
10. A body is dropped and observed to bounce a height greater than the dropping height. Then :
(a) the collision is elastic
(b) there is additional source of energy during collision
(c) it is not possible
(d) this type of phenomenon does not occur in nature.
11. A rocket works on the principle of conservation of :
(a) mass (b) kinetic energy
(c) linear momentum (d) angular momentum.
12. Choose the correct definition of impulse :
(a) impulse is defined as rate of change of momentum of particle
(b) impulse is defined as change in momentum of a particle
(c) impulse is defined as the integral of force with respect to time
(d) both 2 and 3 are correct.
13. A particle of mass m is projected from the ground at an angle θ from vertical. The change in momen-
tum when it is at highest point of its track.
(a) mu sin θ (b) 2 mu sin θ
(c) mu cos θ (d) 2 mu cos θ .
m
u

14. A bullet of mass m fired with velocity u forming an angle
θ with the horizontal and get embedded in a wooden block
of same mass m. The block is placed on smooth surface.
The magnitude horizontal component of impulse is :
(a)
2
θ
cos
mu
(b)
2
θ
sin
mu
(c) θ
cos
mu (d) θ
sin
mu .
15. A bomb projected in a parabolic path under the effect of gravity, explodes in mid air. The centre of
mass of fragments will :
(a) move vertically upwards and then downwards
(b) move vertically downwards
(c) move in irregular path
(d) move in the parabolic path as the unexploded bomb would have moved.

3. OBJECTIVE LEVEL - II
1. Two bodies having masses m1
and m2
and velocities 2
1 u
and
u


collide and form a composite system
of  
2
1
2
2
1
1 m
m
0
u
m
u
m 




. The velocity of the composite system is :
(a) 0 (b) 2
1 u
u



(c) 2
1 u
u


 (d)   2
/
u
u 2
1


 .
2. Six identical balls are lined up along a straight frictionless groove. Two similar balls moving with
speed v along the groove collide with this row on extreme left side end. Then :
(a) One ball from the right end will move on with speed 2v, all the other remains at rest
(b) Two balls from the extreme right will move on with speed v each and the remaining balls will be
at rest
(c) All the balls will start moving to right with speed v/8 each
(d) All the six balls originally at rest will move on with speed u/6 each and the two incident ball will
come to rest.
3. The centre of mass of a body :
(a) Lies always at the geometrical centre (b) Lies always inside the body
(c) Lies always outside the body (d) May lie within or outside the body.
4. A system consists of mass M and m(<M). The centre of mass of the system is ;
(a) At the middle (b) Nearer to M
(c) Nearer to m (d) At the position of large mass.
5. A ball impinges directly on a similar ball at rest. The first ball is brought to rest by the impact. If half
the kinetic energy is lost by impact, what is the value of the coefficient of restitution ?
(a)
2
2
1
(b)
3
1
(c)
2
1
(d)
2
3
.
6. Which one of the following is correct about centre of mass :
(a) It depends on frame of reference
(b) In centre of mass frame momentum of a system is always zero
(c) Internal forces may affect the motion of centre of mass
(d) Centre of mass and centre of gravity are synonymous.
7. All the particles of a body are situated at a distance R from the origin. The distance of the centre of
mass of the body from the origin is :
(a) = R (b)  R
(c) > R (d)  R.

4. 8. An isolated particle of mass m is moving in a horizontal plane (x – y), along the x-axis, at a certain
height above the ground. It suddenly explodes into two fragments of masses m/4 and 3m/4. An
instant later, the smaller fragment is at y = + 15 cm. The larger fragment at this instant is at :
(a) y = - 5 cm (b) y = + 20 cm
(c) y = + 5 cm (d) y = -20 cm.
9. A neutron traveling with a velocity v and kinetic energy E collides elastically head on with the nucleus
of an atom of mass number A at rest. The fraction of total energy retained by the neutron is :
(a)
2
1
A
1
A








(b)
2
1
A
1
A








(c)
2
A
1
A





 
(d)
2
A
1
A





 
.
10. A sphere of mass m moving with a constant velocity u hits another stationary sphere of the same
mass. If e is the coefficient of restitution, then ratio of velocities of the two spheres (First sphere/
Second sphere) after collision will be :
(a) 







e
1
e
1
(b) 







e
1
e
1
(c) 







1
e
1
e
(d) 







1
e
1
e
.
11. AparticleAsuffers an oblique elastic collision with a particle B that is at rest initially, if their masses
are same, then after the collision :
(a) they will move in opposite directions
(b) A continues to move in the original direction while B remains at rest
(c) they will move in mutually perpendicular directions
(d) A comes to rest and B starts moving in the direction of the original motion of A.
12. A loaded spring gun of mass M fires a shot of mass m with a velocity V at an angle of elevation θ .
The gun is initially at rest on a horizontal frictionless surface. Just after firing, the centre of mass of
the gun-shot system :
(a) moves with a velocity
M
m
V
(b) moves with a velocity
M
Vm
cos θ in the horizontal direction
(c) remains at rest
(d) moves with a velocity
 
 
m
M
m
M
V


in the horizontal direction.

5. 13. A steel ball strikes a steel plate placed on a horizontal surface at an angle θ with the vertical. If the
co-efficient of restitution is e, the angle at which the rebound will take place is :
(a) θ (b) 






e
θ
tan
tan 1
(c) θ
tan
e (d) 






θ
tan
e
tan 1
.
14. An earth satellite of mass M circles the earth with speed V. The change in momentum when it goes
halfway around the earth is :
(a) 0 (b) Mv
(c) 2Mv (d)
2
Mv
.
P
t0 2t0
t
15. The magnitude of the momentum of a particle varying with time is
shown in figure. The variation of force acting on the particle is
shown as :
(a)
2t0
F
t
t0
(b)
F
t
t0 2t0
(c)
F
t
t0 2t0
(d)
F
t
t0 2t0
.