Thursday 15 November 2012

CENTRE OF MASS & MOMENTUM

Q.1 Consider a one-dimensional elastic collision between a given incoming body A and a body B initially rest.
How would you choose the mass of B, in comparison to the mass of A, in order that B should recoil with
(a) the greatest speed, (b) the greatest momentum, and (c) the greatest kinetic energy?
Q.2 Can the coefficient of restitution ever be greater that 1?
Q.3 A rocket following a parabolic path through the air suddenly explodes into many pieces. What can you
say about the motion of this system of pieces?
Q.4 If only an external force can change the momentum of the centre of mass of an object, how can the
internal force of the engine accelerate a car?
Q.5 Why does a fielder lower his hand while taking a 'catch'?
Q.6 Why does a gun appear to have a greater 'kick' when fired with the butt held loosely against the shoulder
than when held tightly?
Q.7 Figure shows the position-time graph of a particle of mass m =0.5
kg. Suggest a suitable example to fit the curve. What is the interval
between ten consecutive impulses? What is the magnitude of each
impulse?
Q.8 Do the cm and the cg coincide for a building? For a lake? Under what conditions does the difference
between these two points become insignificant?
Q.9 A car has the same kinetic energy when it is traveling south at 30 m/s as when it is traveling northwest at
30 m/s. Is the momentum of the car the same in both cases? Explain.
Q.10 A truck is accelerating as it speeds down the highway. One inertial frame of reference is attached to the
ground with its origin at a fence post. A second frame of reference is attached to a police car that is
traveling down the highway at constant velocity. Is the momentum of the truck the same in these two
reference frames? Explain. Is the rate of change of the truck's momentum the same in these two frames?
Explain.
Q.11 When a large, heavy truck collides with a passenger car, the occupants of the car are more likely to be
hurt than the truck driver. Why?
Q.12 A glass dropped on the floor is more likely to break if the floor is concrete than if it is wood.Why?
Q.13 A machine gun is fired at a steel plate. Is the average force on the plate from the bullet impact greater if
the bullets bounce off or if they are squashed and stick to the plate? Explain.
Q.14 A net force with x-component
Fx acts on an object from time t1 to time t2. The x-component of the
momentum of the object is the same at t
1 as it is at t2, but Fx is not zero at all times between t1 and t2.
What can you say about the graph of
Fx versus t?
Q.15 In a head-on auto collision, passengers not wearing seat belts can be thrown through the windshield. Use
Newton's laws of motion to explain why this happens.
ONLY ONE OPTION IS CORRECT.
Take approx. 2 minutes for answering each question.
Q.1 What should be the minimum force P to be applied to the string so that
block of mass m just begins to move up the frictionless plane.
(A) Mg tan
2 (B) Mg cot 2 (C)  
1 sin
Mg cos
(D) None
Q.2 Both the blocks shown here are of mass m and are moving with constant
velocity in direction shown in a resistive medium which exerts equal
constant force on both blocks in direction opposite to the velocity. The
tension in the string connecting both of them will be : (Neglect friction)
(A) mg (B) mg/2
(C) mg/3 (D) mg/4
Q.3 A rope of mass 5 kg is moving vertically in vertical position with an upwards force of 100 N acting at the
upper end and a downwards force of 70 N acting at the lower end. The tension at midpoint of the rope is
(A) 100 N (B) 85 N (C) 75 N (D) 105 N
Q.4 Find the acceleration of 3 kg mass when acceleration of 2 kg mass is 2
ms
–2 as shown in figure.
(A) 3 ms
–2 (B) 2 ms–2
(C) 0.5 ms
–2 (D) zero
Q.5 Block of 1 kg is initially in equilibrium and is hanging by two identical springs A
and B as shown in figures. If spring A is cut from lower point at t=0 then, find
acceleration of block in ms
–2 at t = 0.
(A) 5 (B) 10 (C) 15 (D) 0
Q.6 Two masses m and M are attached to the strings as shown in the figure.
If the system is in equilibrium, then
(A) tan
= 1 +
m
2M
(B) tan
= 1 +
M
2m
(C) cot
= 1 +
m
2M
(D) cot
= 1 +
M
2m
Q.7 In the figure shown the velocity of different blocks is shown. The velocity of C is
(A) 6 m/s
(B) 4 m/s
(C) 0 m/s
(D) none of these
Q.8 A stunt man jumps his car over a crater as shown (neglect air resistance)
(A) during the whole flight the driver experiences weightlessness
(B) during the whole flight the driver never experiences weightlessness
(C) during the whole flight the driver experiences weightlessness only at the highest point
(D) the apparent weight increases during upward journey
Q.9 A flexible chain of weight W hangs between two fixed points A & B which are at he same horizontal
level. The inclination of the chain with the horizontal at both the points of support is
. What is the tension
of the chain at the mid point?
(A)
2
W
. cosec
(B)
2
W
. tan
(C)
2
W
cot
(D) none
Q.10 A weight can be hung in any of the following four ways by string of same type. In which case is the string
most likely to break?
(A) A (B) B (C) C (D) D
Question No. 11 to 13 (3 questions)
A particle of mass m is constrained to move on x-axis. A force F acts on the
particle. F always points toward the position labeled E. For example, when the
particle is to the left of E, F points to the right. The magnitude of F is a
constant F except at point E where it is zero.
The system is horizontal. F is the net force acting on the particle. The particle is displaced a distance A
towards left from the equilibrium position E and released from rest at t = 0.
Q.11 What is the period of the motion?
(A)
 
 
F
2Am
4 (B)
 
 
F
2Am
2 (C)
 
 
F
2Am
(D) None
Q.12 Velocity – time graph of the particle is
(A) (B)
(C) (D)
Q.13 Find minimum time it will take to reach from x = –
2
A
to 0.
(A) ( 2 1)
F
mA
2
3
(B) ( 2 1)
F
mA
(C) ( 2 1)
F
mA
2
(D) None
Q.14 Two blocks are connected by a spring. The combination is suspended, at rest, from
a string attatched to the ceiling, as shown in the figure. The string breaks suddenly.
Immediately after the string breaks, what is the initial downward acceleration
of the upper block of mass 2m ?
(A) 0 (B) 3g/2 (C) g (D) 2g
Q.15 A body is placed on a rough inclined plane of inclination
. As the angle is increased from 0° to 90° the
contact force between the block and the plane
(A) remains constant (B) first remains constant than decreases
(C) first decreases then increases (D) first increases then decreases
Q.16 A force
j ˆ 4 i ˆ F  
acts on block shown. The force of friction acting on the block is :
(A) – i ˆ (B) – 1.8
i ˆ
(C) – 2.4 i ˆ (D) – 3 i ˆ
Q.17 If force F is increasing with time and at t = 0 , F = 0 where will slipping
first start?
(A) between 3 kg and 2 kg (B) between 2 kg and 1 kg
(C) between 1 kg and ground (D) both (A) and (B)
Q.18 In the arrangement shown in the figure, mass of the block B and A is 2m and m
respectively. Surface between B and floor is smooth. The block B is connected to
the block C by means of a string pulley system. If the whole system is released,
then find the minimum value of mass of block C so that block A remains stationary
w.r.t. B. Coefficient of friction between A and B is
:
(A)
m
(B) 1
2m 1
 
(C) 1
3m
 
(D) 1
6m
 
Q.19 With what minimum velocity should block be projected from left end A towards end B such that it
reaches the other end B of conveyer belt moving with constant velocity v. Friction coefficient between
block and belt is
.
(A)
gL (B) 2gL
(C) 3
gL (D) 2 gL
Q.20 Block B of mass 100 kg rests on a rough surface of friction coefficient
= 1/3. A rope is tied to block B as shown in figure. The maximum
acceleration with which boy A of 25 kg can climbs on rope without making
block move is :
(A)
3
4g
(B)
3
g
(C)
2
g
(D)
4
3g
Q.21 A block placed on a rough inclined plane of inclination (
=30°) can just be
pushed upwards by applying a force "F" as shown. If the angle of inclination of
the inclined plane is increased to (
= 60°), the same block can just be prevented
from sliding down by application of a force of same magnitude. The coefficient
of friction between the block and the inclined plane is
(A)
3 1
3 1
(B)
3 1
2 3 1
(C)
3 1
3 1
(D) None of these
For Q. 22 to Q.26 refer figure-1.(5 questions)
Q.22 When F = 2N, the frictional force between 5 kg block and ground is
(A) 2N (B) 0
(C) 8 N (D) 10 N
Q.23 When F = 2N, the frictional force between 10 kg block and 5 kg block is
(A) 2N (B) 15 N (C) 10 N (D) None
Q.24 The maximum "F" which will not cause motion of any of the blocks.
(A) 10 N (B) 15 N (C) data insufficient (D) None
Q.25 The maximum acceleration of 5 kg block
(A) 1 m/s
2 (B) 3 m/s2 (C) 0 (D) None
Q.26 The acceleration of 10 kg block when F = 30N
(A) 2 m/s
2 (B) 3 m/s2 (C) 1 m/s2 (D) None
Q.27 A truck starting from rest moves with an acceleration of 5 m/s
2 for 1 sec and
then moves with constant velocity. The velocity w.r.t ground v/s time
graph for block in truck is ( Assume that block does not fall off the truck)
(A) (B) (C) (D) None of these
Q.28 If angular velocity of a disc depends an angle rotated
as = 2 + 2, then its angular acceleration at
= 1 rad is :
(A) 8 rad/sec
2 (B) 10 rad/sec2 (C) 12 rad/sec2 (D) None
Q.29 Tangential acceleration of a particle moving in a circle of radius 1 m varies with
time t as (initial velocity of particle is zero). Time after which total acceleration of
particle makes and angle of 30° with radial acceleration is
(A) 4 sec (B) 4/3 sec
(C) 2
2/3 sec (D) 2 sec
Q.30 The magnitude of displacement of a particle moving in a circle of radius a with constant angular speed
varies with time t as
(A) 2 a sin
t (B) 2a sin
2
t
(C) 2a cos
t (D) 2a cos
2
t
Q.31 A man is standing on a rough (
= 0.5) horizontal disc rotating with constant angular velocity of
5 rad/sec. At what distance from centre should he stand so that he does not slip on the disc?
(A) R
0.2m (B) R > 0.2 m (C) R > 0.5 m (D) R > 0.3 m
Q.32 A car travelling on a smooth road passes through a curved portion of the road in
form of an arc of circle of radius 10 m. If the mass of car is 500 kg, the reaction
on car at lowest point P where its speed is 20 m/s is
(A) 35 kN (B) 30 kN (C) 25 kN (D) 20 kN
Q.33 A pendulum bob is swinging in a vertical plane such that its angular amplitude is less than 90
0. At its
highest point, the string is cut. Which trajectory is possible for the bob afterwards.
(A) (B) (C) (D)
Q.34 A conical pendulum is moving in a circle with angular velocity
as shown. If
tension in the string is T, which of following equations are correct ?
(A) T = m
2l (B) T sin= m2l
(C) T = mg cos
(D) T = m2 l sin
Q.35 A road is banked at an angle of 30° to the horizontal for negotiating a curve of radius 10 3 m. At what
velocity will a car experience no friction while negotiating the curve?
(A) 54 km/hr (B) 72 km/hr (C) 36 km/hr (D) 18 km/hr
Q.36 The ratio of period of oscillation of the conical pendulum to that of the simple pendulum is :
(Assume the strings are of the same length in the two cases and
is the angle made by the string with the
verticla in case of conical pendulum)
(A) cos
(B) cos(C) 1 (D) none of these
Q.37 A particle is moving in a circle :
(A) The resultant force on the particle must be towards the centre.
(B) The cross product of the tangential acceleration and the angular velocity will be zero.
(C) The direction of the angular acceleration and the angular velocity must be the same.
(D) The resultant force may be towards the centre.
Q.38 A particle is moving along the circle x
2 + y2 = a2 in anti clock wise direction. The x–y plane is a rough
horizontal stationary surface. At the point (a cos
, a sin), the unit vector in the direction of friction on the
particle is:
(A) j ˆ sin i ˆ cos
   (B)   j ˆ sin i ˆ cos     (C) j ˆ cos i ˆ sin    (D) j ˆ sin i ˆ cos  
Q.39 Two bodies A & B rotate about an axis, such that angle
A (in radians) covered by first body is proportional
to square of time, &
B (in radians) covered by second body varies linearly. At t = 0, A = B = 0. If A
completes its first revolution in
sec. & B needs 4sec. to complete half revolution then; angular
velocity
A : B at t = 5 sec. are in the ratio
(A) 4 : 1 (B) 20 : 1 (C) 80 : 1 (D) 20 : 4
Q.40 Which vector in the figures best represents the acceleration of a pendulum mass at the intermediate point
in its swing?
(A) (B) (C) (D)
Q.41 The dumbell is placed on a frictionless horizontal table. Sphere A is attached to
a frictionless pivot so that B can be made to rotate about A with constant angular
velocity. If B makes one revolution in period P, the tension in the rod is
(A)
2
2
P
4
Md
(B)
2
2
P
8
Md
(C)
P
4
2Md
(D)
P
2Md
Q.42 Two racing cars of masses m
1 and m2 are moving in circles of radii r1 and r2 respectively. Their speeds
are such that each makes a complete circle in the same time t. The ratio of the angular speeds of the first
to the second car is
(A) 1 : 1 (B) m
1 : m2 (C) r1 : r2 (D) m1m2 : r1r2
Q.43 The graphs below show angular velocity as a function of time. In which one is the magnitude of the
angular acceleration constantly decreasing?
(A) (B) (C) (D)
Q.44 Equal force F (> mg) is applied to string in all the 3 cases. Starting from rest, the point of application of
force moves a distance of 2 m down in all cases. In which case the block has maximum kinetic energy?
(A) 1 (B) 2 (C) 3 (D) equal in all 3 cases
Q.45 A body of mass m accelerates uniformly from rest to a speed v
0 in time t0. The work done on the body
till any time t is
(A)
2
1
mv
0
2
 
2
0
2
t
t
(B)
2
1
mv
0
2

t
t
0 (C) mv0
2
 
 
t
0
t
(D) mv
0
2
3
0
t
t
 
 
Q.46 A man who is running has half the kinetic energy of the boy of half his mass. The man speeds up by
1 m/s and then has the same kinetic energy as the boy. The original speed of the man was
(A)
2 m/s (B) ( 2 – 1) m/s (C) 2 m/s (D) ( 2 + 1) m/s
Q.47 F = 2x
2 – 3x – 2. Choose correct option
(A) x = – 1/2 is position of stable equilibrium (B) x = 2 is position of stable equilibrium
(C) x = – 1/2 is position of unstable equilibrium (D) x = 2 is position of neutral equilibrium
Q.48 A block of mass m is hung vertically from an elastic thread of force constant mg/a. Initially the thread was
at its natural length and the block is allowed to fall freely. The kinetic energy of the block when it passes
through the equilibrium position will be :
(A) mga (B) mga/2 (C) zero (D) 2mga
Q.49 Assume the aerodynamic drag force on a car is proportional to its speed. If the power output from the
engine is doubled, then the maximum speed of the car.
(A) is unchanged (B) increases by a factor of 2
(C) is also doubled (D) increases by a factor of four.
Q.50 A particle is released from rest at origin. It moves under influence of potential field U = x
2 – 3x , kinetic
energy at x = 2 is
(A) 2J (B) 1 J (C) 1.5 J (D) 0 J
Q.51 A force ] j ˆ x i ˆ F
k[y
where k is a positive constant acts on a particle moving in x-y plane starting from
the point (3,5), the particle is taken along a straight line to (5, 7). The work done by the force is :
(A) zero (B) 35 K (C) 20 K (D) 15 K
Q.52 A light spring of length 20 cm and force constant 2 kg/cm is placed vertically on a table.A small block of
mass 1 kg. falls on it. The length h from the surface of the table at which the ball will have the maximum
velocity is
(A) 20 cm (B) 15 cm (C) 10 cm (D) 5 cm
Q.53 The work done in joules in increasing the extension of a spring of stiffness 10 N/cm from 4 cm to 6 cm is:
(A) 1 (B) 10 (C) 50 (D) 100
Q.54 In the figure shown all the surfaces are frictionless, and mass of the block,
m = 1 kg. The block and wedge are held initially at rest. Now wedge is given a
horizontal acceleration of 10 m/s
2 by applying a force on the wedge, so that the
block does not slip on the wedge. Then work done by the normal force in
ground frame on the block in 3 seconds is
(A) 30 J (B) 60 J
(C) 150 J (D) 100 3 J
Q.55 When a conservative force does positive work on a body
(A) the potential energy increases (B) the potential energy decreases
(C) total energy increases (D) total energy decreases
Q.56 The P.E. of a certain spring when stretched from natural length through a distance 0.3 m is10 J. The
amount of work in joule that must be done on this spring to stretch it through an additional distance
0.15 m will be
(A) 10 J (B) 20 J (C) 7.5 J (D) 12.5 J
Q.57 A 1.0 kg block collides with a horizontal weightless spring of force constant
2.75 Nm
–1 as shown in figure. The block compresses the spring 4.0 m from the
rest position. If the coefficient of kinetic friction between the block and horizontal
surface is 0.25, the speed of the block at the instant of collision is
(A) 0.4 ms
–1 (B) 4 ms–1 (C) 0.8 ms–1 (D) 8 ms–1
Question No. 58 to 63 (6 questions)
A block of mass m moving with a velocity v
0 on a smooth horizontal surface strikes and compresses a
spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two
observers:
A
: standing on the horizontal surface B: standing on the block
Q.58 To an observer A, the work done by spring force is
(A) negative but nothing can be said about its magnitude (B) –
2
0
mv
2
1
(C) positive but nothing can be said about its magnitude (D) +
2
0
mv
2
1
Q.59 To an observer A, the work done by the normal reaction N between the block and the spring on the
block is
(A) zero (B) –
2
0
mv
2
1
(C) +
2
0
mv
2
1
(D) none of these
Q.60 To an observer A, the net work done on the block is
(A)
2
mv0 (B) + 2
0
mv (C) – 2
0
mv
2
1
(D) zero
Q.61 According to the observer A
(A) the kinetic energy of the block is converted into the potential energy of the spring
(B) the mechanical energy of the spring-mass system is conserved
(C) the block loses its kinetic energy because of the negative work done by the conservative force of
spring
(D) all the above
Q.62 To an observer B, when the block is compressing the spring
(A) velocity of the block is decreasing (B) retardation of the block is increasing
(C) kinetic energy of the block is zero (D) all the above
Q.63 According to observer B, the potential energy of the spring increases
(A) due to the positive work done by pseudo force
(B) due to the positive work done by normal reaction between spring & wall
(C) due to the decrease in the kinetic energy of the block
(D) all the above
Q.64 A particle originally at rest at the highest point of a smooth vertical circle is slightly displaced. It will leave
the circle at a vertical distance h below the highest point, such that
(A) h = R (B) h = R/3 (C) h = R/2 (D) h = 2R
Q.65 A ball whose size is slightly smaller than width of the tube of radius 2.5 m is projected from bottommost
point of a smooth tube fixed in a vertical plane with velocity of 10 m/s. If N
1 and N2 are the normal
reactions exerted by inner side and outer side of the tube on the ball
(A) N
1> 0 for motion in ABC, N2 > 0 for motion in CDA
(B) N
1> 0 for motion in CDA, N2 > 0 for motion in ABC
(C) N
2> 0 for motion in ABC & part of CDA
(D) N
1 is always zero.
Q.66 A bob attached to a string is held horizontal and released. The tension
and vertical distance from point of suspension can be represented by.
(A) (B) (C) (D)
Q.67 A body of mass 1 kg starts moving from rest at t = 0, in a circular path of radius 8 m. Its kinetic energy
varies as a function of time as : K.E. = 2t
2 Joules, where t is in seconds. Then
(A) tangential acceleration = 4 m/s
2 (B) power of all forces at t = 2 sec is 8 watt
(C) first round is completed in 2 sec. (D) tangential force at t = 2 sec is 4 newton.
Q.68 A small cube with mass M starts at rest at point 1 at a height 4R, where R is the
radius of the circular part of the track. The cube slides down the frictionless
track and around the loop. The force that the track exerts on the cube at point
2 is nearly _____ times the cube's weight Mg.
(A) 1 (B) 2 (C) 3 (D) 4
Q.69 The tube AC forms a quarter circle in a vertical plane. The ball B has an area of cross–section slightly
smaller than that of the tube, and can move without friction through it. B is placed at A and displaced
slightly. It will
(A) always be in contact with the inner wall of the tube
(B) always be in contact with the outer wall of the tube
(C) initially be in contact with the inner wall and later with the outer wall
(D) initially be in contact with the outer wall and later with the inner wall
Question No. 70 to 71 (2 questions)
A spring block system is placed on a rough horizontal floor. The block is pulled towards right to give
spring an elongation less than
K
2
mg
but more than
K
mg
and released.
Q.70 Which of the following laws/principles of physics can be applied on the spring
block system
(A) conservation of mechanical energy (B) conservation of momentum
(C) work energy principle (D) None
Q.71 The correct statement is
(A) The block will cross the mean position.
(B) The block will come to rest when the forces acting on it are exactly balanced
(C) The block will come to rest when the work done by friction becomes equal to the change in energy
stored in spring.
(D) None
Q.72 A particle is rotated in a vertical circle by connecting it to a light rod of length l and keeping the other end
of the rod fixed. The minimum speed of the particle when the light rod is horizontal for which the particle
will complete the circle is
(A) g
l (B) 2gl (C) 3gl (D) none
Q.73 A ball strikes a smooth horizontal ground at an angle of 45° with the vertical. What
cannot be the
possible angle of its velocity with the vertical after the collision. (Assume e
1 ).
(A) 45° (B) 30° (C) 53° (D) 60°
Q .74 A s show n in the figure a body of m ass m m oving vertically w ith speed
3 m /s hits a sm ooth fixed inclined plane and rebounds w ith a velocity v
f in the
horizontal direction. If
of inclined is 30°, the velocity vf will be
(A) 3 m/s (B)
3 m/s
(C) 1 3 m/s (D) this is not possible
Q.75 The system of the wedge and the block connected by a massless spring
as shown in the figure is released with the spring in its natural length.
Friction is absent. maximum elongation in the spring will be
(A)
5k
3Mg
(B)
5k
6Mg
(C)
5k
4Mg
(D)
5k
8Mg
Q.76 Two massless string of length 5 m hang from the ceiling very near to each
other as shown in the figure. Two balls A and B of masses 0.25 kg and 0.5
kg are attached to the string. The ball A is released from rest at a height
0.45 m as shown in the figure. The collision between two balls is completely
elastic. Immediately after the collision, the kinetic energy of ball B is 1 J.
The velocity of ball A just after the collision is
(A) 5 ms
–1 to the right (B) 5 ms–1 to the left
(C) 1 ms
–1 to the right (D) 1 ms–1 to the left
Q.77 A man of mass M stands at one end of a plank of length L which lies at rest on a frictionless surface. The
man walks to other end of the plank. If the mass of the plank is
3
M
, then the distance that the man moves
relative to ground is :
(A)
4
3L
(B)
4
L
(C)
5
4L
(D)
3
L
Q.78 Two balls A and B having masses 1 kg and 2 kg, moving with speeds 21 m/s and 4 m/s respectively in
opposite direction, collide head on. After collision A moves with a speed of 1 m/s in the same direction,
then the coefficient of restitution is
(A) 0.1 (B) 0.2 (C) 0.4 (D) None
Q.79 A particle of mass 3m is projected from the ground at some angle with horizontal. The horizontal range
is R. At the highest point of its path it breaks into two pieces m and 2m. The smaller mass comes to rest
and larger mass finally falls at a distance x from the point of projection where x is equal to
(A)
4
3R
(B)
2
3R
(C)
4
5R
(D) 3R
Q.80 A man weighing 80 kg is standing at the centre of a flat boat and he is 20 m from the shore. He walks 8 m
on the boat towards the shore and then halts. The boat weight 200 kg. How far is he from the shore at
the end of this time ?
(A) 11.2 m (B) 13.8 m (C) 14.3 m (D) 15.4 m
Q.81 From a circle of radius a, an isosceles right angled triangle with the hypotenuse as the diameter of the
circle is removed. The distance of the centre of gravity of the remaining position from the centre of the
circle is
(A) 3(
– 1)a (B)
6
(
 1)a
(C) 3( 1)
a
 
(D) 3( 1)
a
 
Q.82 A truck moving on horizontal road towards east with velocity 20 ms
–1 collides elastically with a light ball
moving with velocity 25 ms
–1 along west. The velocity of the ball just after collision
(A) 65 ms
–1 towards east (B) 25 ms–1 towards west
(C) 65 ms
–1 towards west (D) 20 ms–1 towards east
Question No. 83 to 84 (2 questions)
A uniform chain of length 2L is hanging in equilibrium position, if end B is given a
slightly downward displacement the imbalance causes an acceleration. Here pulley is
small and smooth & string is inextensible
Q.83 The acceleration of end B when it has been displaced by distance x, is
(A)
L
x
g (B)
L
2
x
g (C)
2
x
g (D) g
Q.84 The velocity v of the string when it slips out of the pulley (height of pulley from floor > 2L)
(A)
2
gL
(B) 2gL (C) gL (D) none of these
Q.85 A small sphere is moving at a constant speed in a vertical circle. Below is a list of quantities that could be
used to describe some aspect of the motion of the sphere.
I – kinetic energy
II – gravitational potential energy
III – momentum
Which of these quantities will change as this sphere moves around the circle?
(A) I and II only (B) I and III only (C) III only (D) II and III only
Q.86 Which of the following graphs represents the graphical relation between momentum (p) and kinetic
energy (K) for a body in motion?
(A) (B) (C) (D) none
Q.87 A small bucket of mass M kg is attached to a long inextensible cord of length L m . The bucket is
released from rest when the cord is in a horizontal position. At its lowest position, the bucket scoops up
m kg of water and swings up to a height h. The height h in meters is
(A) L
M m
M
2


(B) L
M m
M


(C) L
M
M m
2


 
(D) L
M
M m


 
Q.88 In the figure shown a hole of radius 2 cm is made in a semicircular disc of radius 6
at a distance 8 cm from the centre C of the disc. The distance of the centre of mass
of this system from point C is :
(A) 4 cm (B) 8 cm (C) 6 cm (D) 12 cm
Q.89 In the figure shown, the two identical balls of mass M and radius R each, are placed in
contact with each other on the frictionless horizontal surface. The third ball of mass M
and radius R/2, is coming down vertically and has a velocity = v
0 when it simultaneously
hits the two balls and itself comes to rest. Then, each of the two bigger balls will move
after collision with a speed equal to
(A) 4v
0 5 (B) 2v0 5 (C) v0 5 (D) None
Q.90 In the
above, suppose that the smaller ball does not stop after collision, but continues to move downwards
with a speed= v
0/2, after the collision. Then, the speed of each bigger ball after collision is
(A) 4v
0 5 (B) 2v0 5 (C) v0 2 5 (D) None
Q.91 A body of mass ‘m’ is dropped from a height of ‘h’. Simultaneously another body of mass 2m is thrown
up vertically with such a velocity v that they collide at the height h/2. If the collision is perfectly inelastic,
the velocity at the time of collision with the ground will be :
(A)
4
5g h
(B) g h (C)
4
g h
(D)
3
10gh
Q.92 In the figure (i), (ii) & (iii) shown the objects A, B & C are of
same mass. String, spring & pulley are massless. C strikes B
with velocity ‘u’ in each case and sticks to it. The ratio of velocity
of B in case (i) to (ii) to (iii) is
(A) 1 : 1: 1 (B) 3 : 3 : 2
(C) 3 : 2 : 2 (D) none of these
Q.93 Centre of mass of two thin uniform rods of same length but made up of
different materials & kept as shown , can be, if the meeting point is the
origin of co-ordinates
(A) (L/2, L/2) (B) (2L/3, L/2)
(C) (L/3, L/3) (D) (L/3, L/6)
Q.94 A force exerts an impulse I on a particle changing its speed from u to 2u. The applied force and the initial
velocity are oppositely directed along the same line. The work done by the force is
(A)
I u
2
3
(B)
I u
2
1
(C) I u (D) 2 I u
Q.95 In the diagram shown, no friction at any contact surface. Initially, the spring has no deformation. What
will be the maximum deformation in the spring? Consider all the strings to be sufficiency large. Consider
the spring constant to be K.
(A) 4F / 3K (B) 8F / 3K
(C) F / 3K (D) none
Q.96 In a smooth stationary cart of length d, a small block is projected along it's length with velocity v towards
front. Coefficient of restitution for each collision is e. The cart rests on a smooth ground and can move
freely. The time taken by block to come to rest w.r.t. cart is
(A)
(1 e)v
ed
(B) (1 e)v
ed
(C)
e
d
(D) infinite
Q.97 An open water tight railway wagon of mass 5 × 10
3 kg coasts at an initial velocity 1.2 m/s without friction
on a railway track. Rain drops fall vertically downwards into the wagon. The velocity of the wagon after
it has collected 10
3 kg of water will be
(A) 0.5 m/s (B) 2 m/s (C) 1 m/s (D) 1.5 m/s
Q.98 A parallel beam of particles of mass m moving with velocity v impinges on a wall at an angle
to its
normal . The number of particles per unit volume in the beam is n . If the collision of particles with the
wall is elastic, then the pressure exerted by this beam on the wall is :
(A) 2 mnv
2 cos (B) 2 mnv2 cos2 (C) 2 mnv cos (D) 2 mnv cos2
Q.99 A rocket of mass 4000 kg is set for vertical firing. How much gas must be ejected per second so that the
rocket may have initial upwards acceleration of magnitude 19.6 m/s
2. [Exhaust speed of fuel = 980 m/s.]
(A) 240 kg s
–1 (B) 60 kg s–1 (C) 120 kg s–1 (D) None
Q.100 Three blocks are initially placed as shown in the figure. Block A has mass m and initial velocity v to the
right. Block B with mass m and block C with mass 4m are both initially at rest. Neglect friction. All
collisions are elastic. The final velocity of block A is
(A) 0.6v to the left (B) 1.4v to the left
(C) v to the left (D) 0.4v to the right
Q.101 There are some passengers inside a stationary railway compartment. The track is frictionless. The centre
of mass of the compartment itself (without the passengers) is C
1, while the centre of mass of the
'compartment plus passengers' system is C
2. If the passengers move about inside the compartment along
the track.
(A) both C
1 and C2 will move with respect to the ground
(B) neither C
1 nor C2 will move with respect to the ground
(C) C
1 will move but C2 will be stationary with respect to the ground
(D) C
2 will move but C1 will be stationary with respect to the ground
Q.102 A block of mass m starts from rest and slides down a frictionless semi–circular
track from a height h as shown. When it reaches the lowest point of the track,
it collides with a stationary piece of putty also having mass m. If the block and
the putty stick together and continue to slide, the maximum height that the
block-putty system could reach is:
(A) h/4 (B) h/2 (C) h (D) independent of h
Q.103 A boy hits a baseball with a bat and imparts an impulse J to the ball. The boy hits the ball again with the
same force, except that the ball and the bat are in contact for twice the amount of time as in the first hit.
The new impulse equals:
(A) half the original impulse (B) the original impulse
(C) twice the original impulse (D) four times the original impulse
Q.104 Two billiard balls undergo a head-on collision. Ball 1 is twice as heavy as ball 2. Initially, ball 1 moves
with a speed v towards ball 2 which is at rest. Immediately after the collision, ball 1 travels at a speed of
v/3 in the same direction. What type of collision has occured?
(A) inelastic (B) elastic
(C) completely inelastic (D) Cannot be determined from the information given
Question No. 105 to 108 (4 questions)
A small ball B of mass m is suspended with light inelastic string of length L from
a block A of same mass m which can move on smooth horizontal surface as
shown in the figure. The ball is displaced by angle
from equilibrium position
& then released.
Q.105 The displacement of block when ball reaches the equilibrium position is
(A)
2
L
sin
(B) Lsin
(C) L (D) none of these
Q.106 Tension in string when it is vertical, is
(A) mg (B) mg(2–cos
) (C) mg (3 – 2cos) (D) none of these
Q.107 Maximum velocity of block during subsequent motion of the system after release of ball is
(A) [gl (1-cos
)]1/2 (B) [2gl(1–cos)]1/2
(C) [glcos
]1/2 (D) informations are insufficient to decide
Q.108 The displacement of centre of mass of A + B system till the string becomes vertical is
(A) zero (B) (1 cos )
2
L
  (C) (1 sin )
2
L
  (D) none of these
Q.109 A system of N particles is free from any external forces.
(a) Which of the following is true for the magnitude of the total momentum of the system?
(A) It must be zero
(B) It could be non–zero, but it must be constant
(C) It could be non–zero, and it might not be constant
(D) The answer depends on the nature of the internal forces in the system
(b) Which of the following must be true for the sum of the magnitudes of the momenta of the individual
particles in the system?
(A) It must be zero
(B) It could be non–zero, but it must be constant
(C) It could be non–zero, and it might not be constant
(D) It could be zero, even if the magnitude of the total momentum is not zero
Q.110 An isolated rail car of mass M is moving along a straight, frictionless track at an initial speed v
0. The car
is passing under a bridge when a crate filled with N bowling balls, each of mass m, is dropped from the
bridge into the bed of the rail car. The crate splits open and the bowling balls bounce around inside the
rail car, but none of them fall out.
(a) Is the momentum of the rail car + bowling balls system conserved in this collision?
(A) Yes, the momentum is completely conserved.
(B) Only the momentum component in the vertical direction is conserved.
(C) Only the momentum component parallel to the track is conserved.
(D) No components are conserved.
(b) What is the average speed of the rail car + bowling balls system some time after the collision?
(A) (M + Nm)v
0/M (B) Mv0/(Nm + M) (C) Nmv0/M
(D) The speed cannot be determined because there is not enough information
Question No. 111 to 115 (5 questions)
Two persons of mass m
1 and m2 are standing at the two ends A and B
respectively, of a trolley of mass M as shown.
Q.111 When the person standing at A jumps from the trolley towards left with u
rel with respect to the trolley,
then
(A) the trolley moves towards right
(B) the trolley rebounds with velocity
m m M
m u
1 2
1 rel
 
(C) the centre of mass of the system remains stationary
(D) all the above
Q.112 When only the person standing at B jumps from the trolley towards right while the person at A keeps
standing, then
(A) the trolley moves towards left
(B) the trolley moves with velocity
m m M
m u
1 2
2 rel
 
(C) the centre of mass of the system remains stationary
(D) all the above
Q.113 When both the persons jump simultaneously with same speed then
(A) the centre of mass of the system remains stationary
(B) the trolley remains stationary
(C) the trolley moves toward the end where the person with heavier mass is standing
(D) None of these
Q.114 When both the persons jump simultaneously with u
rel with respect to the trolley, then the velocity of the
trolley is
(A) m m M
|m m | u
1 2
1 2 rel
 
(B)
M
|m m | u
1 2 rel
(C) m M
m u
m M
m u
1
2 rel
2
1 rel
(D) none of these
Q.115 Choose the incorrect statement, if m
1 = m2 = m and both the persons jump one by one, then
(A) the centre of mass of the system remains stationary
(B) the final velocity of the trolley is in the direction of the person who jumps first
(C) the final velocity of the trolley is
 
 
M 2m
mu
M m
mu
rel rel
(D) none of these
Q.116 A ball is dropped from a height h. As it bounces off the floor, its speed is 80 percent of what it was just
before it hit the floor. The ball will then rise to a height of most nearly
(A) 0.80 h (B) 0.75 h (C) 0.64 h (D) 0.50 h
Q.117 A ball is thrown vertically downwards with velocity 2gh from a height h. After colliding with the
ground it just reaches the starting point. Coefficient of restitution is
(A)
1 2 (B) 1/2 (C) 1 (D) 2
Q.118 A ball is dropped from height 5m. The time after which ball stops rebounding if coefficient of restitution
between ball and ground e = 1/2, is
(A) 1 sec (B) 2 sec (C) 3 sec (D) infinite
Q.119 A ball is projected from ground with a velocity V at an angle
to the vertical. On its path it makes an
elastic collison with a vertical wall and returns to ground. The total time of flight of the ball is
(A) g
2vsin
(B) g
2vcos
(C) g
vsin 2
(D) g
v cos
ONE OR MORE THAN ONE OPTION MAY BE CORRECT
Take approx. 3 minutes for answering each question.
Q.1 A student calculates the acceleration of m
1 in figure shown as
a
1 =
1 2
1 2
m m
(m m )g
. Which assumption is not required to do this calculation.
(A) pulley is frictionless (B) string is massless
(C) pulley is massless (D) string is inextensible
Q.2 Which graph shows best the velocity-time graph for an object launched vertically into the air when air
resistance is given by | D | = bv? The dashed line shows the velocity graph if there were no air resistance.
(A) (B) (C) (D)
Q.3 Two men of unequal masses hold on to the two sections of a light rope passing
over a smooth light pulley. Which of the following are possible?
(A) The lighter man is stationary while the heavier man slides with some acceleration
(B) The heavier man is stationary while the lighter man climbs with some acceleration
(C) The two men slide with the same acceleration in the same direction
(D) The two men move with accelerations of the same magnitude in opposite directions
Q.4 Adjoining figure shows a force of 40 N acting at 30° to the horizontal on a body
of mass 5 kg resting on a smooth horizontal surface. Assuming that the
acceleration of free–fall is 10 ms
–2, which of the following statements A, B, C,
D, E is (are) correct?
[1] The horizontal force acting on the body is 20 N
[2] The weight of the 5 kg mass acts vertically downwards
[3] The net vertical force acting on the body is 30 N
(A) 1, 2, 3 (B) 1, 2 (C) 2 only (D) 1 only
Q.5 For ordinary terrestrial experiments, which of the following observers below are inertial.
(A) a child revolving in a " giant wheel".
(B) a driver in a sports car moving with a constant high speed of 200 km/h on a straight road.
(C) the pilot of an aeroplane which is taking off.
(D) a cyclist negotiating a sharp turn.
Q.6 The coefficient of friction between 4kg and 5 kg blocks is 0.2
and between 5kg block and ground is 0.1 respectively. Choose
the correct statements
(A) Minimum force needed to cause system to move is 17N
(B) When force is 4N static friction at all surfaces is 4N to keep system at rest
(C) Maximum acceleration of 4kg block is 2m/s
2
(D) Slipping between 4kg and 5 kg blocks start when F is 17N
Q.7 In a tug–of–war contest, two men pull on a horizontal rope from opposite sides. The winner will be the
man who
(A) exerts greater force on the rope
(B) exerts greater force on the ground
(C) exerts a force on the rope which is greater than the tension in the rope
(D) makes a smaller angle with the vertical
Q.8 A man pulls a block heavier than himself with a light horizontal rope. The coefficient of friction is the same
between the man and the ground, and between the block and the ground
(A) The block will not move unless the man also moves
(B) The man can move even when the block is stationary
(C) If both move, the acceleration of the man is greater than the acceleration of the block
(D) None of the above assertions is correct
Question No. 9 to 10 (2 questions)
In figure, two blocks M and m are tied together with an inextensible and light string. The
mass M is placed on a rough horizontal surface with coefficient of friction
and the
mass m is hanging vertically against a smooth vertical wall.
The pulley is frictionless.
Q.9 Choose the correct statement(s)
(A) The system will accelerate for any value of m
(B) The system will accelerate only when m > M
(C) The system will accelerate only when m >
M
(D) Nothing can be said
Q.10 Choose the correct statement(s) related to the tension T in the string
(A) When m <
M, T = mg (B) When m < M, T = Mg
(C) When m >
M, Mg < T < mg (D) When m > M, mg < T < Mg
Question No. 11 to 14 (4 questions)
Imagine a situation in which the horizontal surface of block M
0 is smooth
and its vertical surface is rough with a coefficient of friction
.
Q.11 Identify the correct statement(s)
(A) If F = 0, the blocks cannot remain stationary
(B) For one unique value of F, the blocks M and m remain stationary with respect to M
0
(C) The limiting friction between m and M
0 is independent of F
(D) There exist a value of F at which friction force is equal to zero
Q.12 In
above problem, choose the correct value(s) of F which the blocks M and m remain stationary with
respect to M
0
(A) (M
0 + M + m)
g
(B)
M m
m(M M m)g
0
 
 
(C) (M
0 + M + m)
M
mg
(D) none of these
Q.13 Consider a special situation in which both the faces of the block M
0 are
smooth, as shown in adjoining figure. Mark out the correct statement(s)
(A) If F = 0, the blocks cannot remain stationary
(B) For one unique value of F, the blocks M and m remain stationary
with respect to block M
0
(C) There exists a range of F for which blocks M and m remain stationary with respect to block M
0
(D) Since there is no friction, therefore, blocks M and m cannot be in equilibrium with respect to M
0
Q.14 In
above problem, the value(s) of F for which M and m are stationary with respect to M0
(A) (M
0 + M + m)g (B) (M0 + M + m)
M
mg
(C) (M
0 + M + m)
m
Mg
(D) none of these
Q.15 A particle with constant total energy E moves in one dimension in a region where the potential energy is
U(x). The speed of the particle is zero where
(A) U(x) = E (B) U(x) = 0 (C)
dx
dU(x)
= 0 (D)
2
2
dx
d U(x)
= 0
Q.16 A block of mass m slides down a plane inclined at an angle
. Which of the following will NOT increase
the energy lost by the block due to friction?
(A) Increasing the angle of inclination (B) Increasing the distance that the block travels
(C) Increasing the accelertion due to gravity (D) Increasing the mass of the block
Q.17 The potential energy in joules of a particle of mass 1 kg moving in a plane is given by U = 3x + 4y, the
position coordinates of the point being x and y, measured in metres. If the particle is initially at rest at
(6,4), then
(A) its acceleration is of magnitude 5 m/s
2
(B) its speed when it crosses the y-axis is 10 m/s
(C) it crosses the y-axis (x = 0) at y = -4
(D) it moves in a straight line passing through the origin (0,0)
Q.18 A box of mass m is released from rest at position 1 on the frictionless curved
track shown. It slides a distance d along the track in time t to reach position 2,
dropping a vertical distance h. Let v and a be the instantaneous speed and
instantaneous acceleration, respectively, of the box at position 2. Which of the
following equations is valid for this situation?
(A) h = vt (B) h = (1/2)gt
2 (C) d = (1/2)at2 (D) mgh = (1/2)mv2
Q.19 A ball of mass m is attached to the lower end of light vertical spring of force constant k. The upper end
of the spring is fixed. The ball is released from rest with the spring at its normal (unstretched) length,
comes to rest again after descending through a distance x.
(A) x = mg/k
(B) x = 2 mg/k
(C) The ball will have no acceleration at the position where it has descended through x/2.
(D) The ball will have an upward acceleration equal to g at its lowermost position.
Q.20 A cart moves with a constant speed along a horizontal circular path. From the cart, a particle is thrown
up vertically with respect to the cart
(A) The particle will land somewhere on the circular path
(B) The particle will land outside the circular path
(C) The particle will follow an elliptical path
(D) The particle will follow a parabolic path
Question No. 21 to 23 (3 questions)
A particle of mass m is released from a height H on a smooth curved
surface which ends into a vertical loop of radius R, as shown
Q.21 Choose the correct alternative(s) if H = 2R
(A) The particles reaches the top of the loop with zero velocity
(B) The particle cannot reach the top of the loop
(C) The particle breaks off at a height H = R from the base of the loop
(D) The particle break off at a height R < H < 2R
Q.22 If
is instantaneous angle which the line joining the particle and the centre of the loop makes with the
vertical, then identify the correct statement(s) related to the normal reaction N between the block and
the surface
(A) The maximum value N occurs at
= 0
(B) The minimum value of N occurs at N =
for H > 5R/2
(C) The value of N becomes negative for
/2 < < 3/2
(D) The value of N becomes zero only when
  /2
Q.23 The minimum value of H required so that the particle makes a complete vertical circle is given by
(A) 5 R (B) 4 R (C) 2.5 R (D) 2 R
Q.24 A particle moving with kinetic energy = 3 joule makes an elastic head on collision with a stationary
particle which has twice its mass during the impact.
(A) The minimum kinetic energy of the system is 1 joule.
(B) The maximum elastic potential energy of the system is 2 joule.
(C) Momentum and total kinetic energy of the system are conserved at every instant.
(D) The ratio of kinetic energy to potential energy of the system first decreases and then increases.
Q.25 Two balls A and B having masses 1 kg and 2 kg, moving with speeds 21 m/s and 4 m/s respectively in
opposite direction, collide head on. After collision A moves with a speed of 1 m/s in the same direction,
then correct statements is :
(A) The velocity of B after collision is 6 m/s opposite to its direction of motion before collision.
(B) The coefficient of restitution is 0.2.
(C) The loss of kinetic energy due to collision is 200 J.
(D) The impulse of the force between the two balls is 40 Ns.
Q.26 An object comprises of a uniform ring of radius R and its uniform chord AB (not
necessarily made of the same material) as shown. Which of the following can
not be the centre of mass of the object
(A) (R/3, R/3) (B) (R/3, R/2)
(C) (R/4, R/4) (D) (R 2 , R 2 )
Q.27 Consider following statements
[1] CM of a uniform semicircular disc of radius R = 2R/
from the centre
[2] CM of a uniform semicircular ring of radius R = 4R/3
from the centre
[3] CM of a solid hemisphere of radius R = 4R/3
from the centre
[4] CM of a hemisphere shell of radius R = R/2 from the centre
Which statements are correct?
(A) 1, 2, 4 (B) 1, 3, 4 (C) 4 only (D) 1, 2 only
Q.28 The diagram to the right shows the velocity-time graph for two
masses R and S that collided elastically. Which of the following
statements is true?
(I) R and S moved in the same direction after the collision.
(II) Kinetic energy of the system (R & S) is minimum at t = 2 milli sec.
(III) The mass of R was greater than mass of S.
(A) I only (B) II only (C) I and II only (D) I, II and III
Q.29 In an inelastic collision,
(A) the velocity of both the particles may be same after the collision
(B) kinetic energy is not conserved
(C) linear momentum of the system is conserved.
(D) velocity of separation will be less than velocity of approach.
Q.30 Two identical balls are interconnected with a massless and inextensible thread. The system is in gravity
free space with the thread just taut. Each ball is imparted a velocity v, one towards the other ball and the
other perpendicular to the first, at t = 0. Then,
(A) the thread will become taut at t = (L/v)
(B) the thread will become taut at some time t < (L/v).
(C) the thread will always remain taut for t > (L/v).
(D) the kinetic energy of the system will always remain mv
2.
Q.31 Two blocks A (5kg) and B(2kg) attached to the ends of a spring constant
1120N/m are placed on a smooth horizontal plane with the spring
undeformed. Simultaneously velocities of 3m/s and 10m/s along the
line of the spring in the same direction are imparted to A and B
then
(A) when the extension of the spring is maximum the velocities of A and B are zero.
(B) the maximum extension of the spring is 25cm.
(C) maximum extension and maximum compression occur alternately.
(D) the maximum compression occur for the first time after 56
sec.
Q.32 In a one–dimensional collision between two particles, their relative velocity is
1 v
before the collision and
2
v
after the collision
(A)
1 v
=
2 v
if the collision is elastic (B)
1 v
= –
2 v
if the collision is elastic
(C)
| v | 2
= | v |
1
in all cases (D)
1 v
= –k
2 v
in all cases, where k
1
Q.33 An isolated rail car originally moving with speed v
0 on a straight, frictionles, level track contains a large
amount of sand. A release valve on the bottom of the car malfunctions, and sand begins to pour out
straight down relative to the rail car.
(a) Is momentum conserved in this process?
(A) The momentum of the rail car alone is conserved
(B) The momentum of the rail car + sand remaining within the car is conserved
(C) The momentum of the rail car + all of the sand, both inside and outside the rail car, is conserved
(D) None of the three previous systems have momentum conservation
(b) What happens to the speed of the rail car as the sand pours out?
(A) The car begins to roll faster
(B) The car maintains the same speed
(C) The car begins to slow down
(D) The problem cannot be solved since momentum is not conserved
Question No. 34 to 40 (7 questions)
A particle of mass m moving horizontally with v
0 strikes a smooth wedge of mass
M, as shown in figure. After collision, the ball starts moving up the
inclined face of the wedge and rises to a height h.
Q.34 The final velocity of the wedge v
2 is
(A)
M
mv
0 (B)
M m
mv
0
(C) v
0 (D) insufficient data
Q.35 When the particle has risen to a height h on the wedge, then choose the correct alternative(s)
(A) The particle is stationary with respect to ground
(B) Both are stationary with respect to the centre of mass
(C) The kinetic energy of the centre of mass remians constant
(D) The kinetic energy with respect to centre of mass is converted into potential energy
Q.36 The maximum height h attained by the particle is
(A)
2g
v
m M
m
2
0

(B)
2g
v
M
m
2
0

(C)
2g
v
m M
M
2
0

(D) none of these
Q.37 Identify the correct statement(s) related to the situation when the particle starts moving downward.
(A) The centre of mass of the system remains stationary
(B) Both the particle and the wedge remain stationary with respect to centre of mass
(C) When the particle reaches the horizontal surface it velocity relative to the wedge is v
0
(D) None of these
Q.38 Suppose the particle when reaches the horizontal surfaces, its velocity with
respect to ground is v
1 and that of wedge is v2. Choose the correct
statement(s)
(A) mv
1 = Mv2 (B) Mv2 – mv1 = mv0 (C) v1 + v2 = v0 (D) v1 + v2 < v0
Q.39 Choose the correct statement(s) related to particle m
(A) Its kinetic energy is K
f = gh
m M
mM


(B) v
1 = v0


M m
M m
(C) The ratio of its final kinetic energy to its initial kinetic energy is
i
K
K
f
=
2
m M
M


(D) It moves opposite to its initial direction of motion
Q.40 Choose the correct statement related to the wedge M
(A) Its kinetic energy is K
f = gh
m M
4m
2
 
 
(B) v
2 = 0 v
m M
2m


(C) Its gain in kinetic energy is
K =  
 
(m
M)2
4mM


2
0
mv
2
1
(D) Its velocity is more than the velocity of centre of mass
ONLY ONE OPTION IS CORRECT.
Take approx. 2 minutes for answering each question.
Q.1 A Q.2 B Q.3 B Q.4 B Q.5 A Q.6 A Q.7 B
Q.8 A Q.9 C Q.10 C Q.11 A Q.12 A Q.13 B Q.14 B
Q.15 B Q.16 A Q.17 C Q.18 C Q.19 B Q.20 B Q.21 C
Q.22 A Q.23 A Q.24 A Q.25 C Q.26 A Q.27 C Q.28 C
Q.29 C Q.30 B Q.31 A Q.32 C Q.33 C Q.34 A Q.35 C
Q.36 B Q.37 D Q.38 C Q.39 C Q.40 B Q.41 B Q.42 A
Q.43 A Q.44 C Q.45 A Q.46 D Q.47 A Q.48 B Q.49 B
Q.50 A Q.51 C Q.52 B Q.53 A Q.54 C Q.55 B Q.56 D
Q.57 D Q.58 B Q.59 B Q.60 C Q.61 D Q.62 C Q.63 B
Q.64 B Q.65 C Q.66 A Q.67 B Q.68 C Q.69 C Q.70 C
Q.71 C Q.72 B Q.73 B Q.74 B Q.75 B Q.76 D Q.77 B
Q.78 B Q.79 C Q.80 C Q.81 C Q.82 A Q.83 A Q.84 C
Q.85 D Q.86 D Q.87 A Q.88 B Q.89 C Q.90 C Q.91 D
Q.92 B Q.93 D Q.94 B Q.95 B Q.96 D Q.97 C Q.98 B
Q.99 C Q.100 A Q.101 C Q.102 A Q.103 C Q.104 B Q.105 A
Q.106 D Q.107 A Q.108 B Q.109(a) B (b) C Q.110(a) C (b) B
Q.111 D Q.112 D Q.113 A Q.114 A Q.115 D Q.116 C Q.117 A
Q.118 C Q.119 B
ONE OR MORE THAN ONE OPTION MAY BE CORRECT
Take approx. 3 minutes for answering each question.
Q.1 C Q.2 B Q.3 A,B,D Q.4 C
Q.5 B Q.6 C Q.7 B Q.8 A,B,C
Q.9 C Q.10 A.C Q.11 A,D Q.12 B,C
Q.13 A,B Q.14 B Q.15 A Q.16 A
Q.17 A,B,C Q.18 D Q.19 B,C,D Q.20 B,D
Q.21 B,D Q.22 A,B,D Q.23 C Q.24 A,B,D
Q.25 A,B,C Q.26 B,D Q.27 C Q.28 D
Q.29 A,B,C,D Q.30 A,C Q.31 B,C Q.32 B,D
Q.33(a) A,C (b) B Q.34 B Q.35 B,D Q.36 C
Q.37 C Q.38 B,C Q.39 B Q.40 A,B,C,D