S.

No Questions
Q1 A system consisting of two objects has a total momentum of (18 kgm/sec)i and
its center of mass has the velocity of (3 m/s)i.One of the object has the mass 4
kg and velocity (1.5 m/s)i.The mass and velocity of the other objects are
(a) 2 kg, (6 m/s)i
(b) 2 kg, (-6 m/s)i
(c) 2 kg, (3 m/s)i
(d) 2 kg, (-3 m/s)I

Q2 Two masses constrained to move in a horizontal plane collide. Given initially

that M 1 = 85gm and M2 = 200gm, v1 = 6.4i cm/sec and v2 = -6.7i - 2j cm/sec.
i and j are the unit vectors across x and y axis respectively

Find the Velocity of Center of mass

(a) -2.8i - 1.4j
(b) 2.8i + 1.4j
(c) 2 i + 1.4j
(d) none of the above
Find the total Linear Momentum of the system
(a) -798i - 400j
(b) -796i + 400j
(c) 600i + 400j
(d) none of the above

Q3 A stationary body of mass 3 kg explodes into three equal parts.Two of the

pieces fly off at right angles to each other with the velocities 2i m/s and 3j m/s.If
the explosion takes place in 10-3 sec.find out the average force action on the
third piece in N
(a) (-2i-3j)103
(b) (2i+3j)103
(c) (2i-3j)10-3
(d) none of these

4 Two masses m1 and m2 separated by thin rod of length L. The system is shown
below

The rod mass can be neglected

The system is thrown into the air. It is assumed only gravitational forces are
acting and frictional forces are assumed to be null
Which of the following statement is false?

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 (a) The center of mass of the system will follow a parabolic path
(b) dptotaldt=m1g+m2gdptotaldt=m1g+m2g
(c) The acceleration of the center of mass will be vertically downward and equal
to g
(d) None of these

5 Which of the following statements are correct?

(a) Centre of mass of a body always coincides with the centre of gravity of the body.
(b) Centre of mass of a body is the point at which the total gravitational torque on the
body is zero.
(c) A couple on a body produce both translational and rotational motion in a body.
(d) Mechanical advantage smaller than one means that small effort can be used to lift a
large load.

6 The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of
mass 4kg. (The coordinates of the same are shown in figure) are:

(0.75m,1.75m)

7 A rigid massless rod of length 3l has two masses attached art each end as shown in the
figure. The rod is pivoted at point P on the horizontal position, its instantaneous angular
acceleration will be:

Ans
g/13l

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8 A mass of man m standing on a block of mass M. The system is at rest. The
man moves relative in x direction to the block with velocity v' and then stops.

Find the Velocity of Center of mass

(a) v'
(b) 0
(c) mv′)/(M+m)
(d) None of the above

Find the displacement of block relative to ground if the displacement of the man
with respect to block is xi
(a) −mxi/M+m
(b) mxi /M+m
(c) xi
(d) none of the above
9 10 objects of mass m0,2 m0,3 m0………………….10 m0 are placed on the x axis
at
(L,0),(2L,0)……(10L,0).Find the Center of mass of the system
Ans- 7L
10 Two blocks of masses 10 kg and 4 kg are con-nected by a spring of negligible mass and
placed on a frictionless horizontal surface. An impulse gives a velocity of 14 m/s to the
heavier block in the direction of the lighter block. The velocity of the centre of mass is

(a) 30 m/s

(b) 20 m/s

(c) 10 m/s

(d) 5 m/s
11 A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their
collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms4. Which
of the following statements(s) are correct for the system of these two masses

(a)The total momentum of the system is 5 kg ms–1

(b) The momentum of 5kg mass after the collision is 4kg ms-1

(c) The kinetic energy of the centre of mass is 0.75 J

(d) The total kinetic energy of the system is 4 J

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12 A circular plate of uniform thickness has a diameter of 56cm. A circular portion of
diameter 42cm is removed from one edge of the plate . Find the position of the centre
of mass of the remaining portion from the center of bigger disc.
Ans-9 cm
13 A particle of mass m moving in the x-direction with speed 2v is hit by another particle
of mass 2m moving in the y-direction with speed v. If the collisions are perfectly
inelastic, the percentage loss in the energy during the collision is close to

(a) 56%

(b) 62%

(c) 44%

(d) 50%
14 A pulley fixed to the ceiling carries a string with blocks of mass m and 3 m attached to
its ends. The masses of string and pulley are negligible. When the system is released,
its centre of mass moves with what acceleration?
A) 0

B) −g/4

C) g/2

D) −g/2
15 A ball rolls without slipping. The radius of gyration of the ball about an axis passing
through its centre of mass is K. If radius of the ball be R, then the fraction of total
energy associated with its rotational energy will be
A)K2/R2

B) K2/(K2+R2)

C) R2/(K2+R2)

D) (K2+R2)/K2

16
A solid sphere, disc and solid cylinder all of the same mass and made of the
same material are allowed to roll down (from rest) on an inclined plane,
then

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 A) solid sphere reaches the bottom first

B) solid sphere reaches the bottom last

C) disc will reach the bottom first

D) all reach the bottom at the same time

17 A solid cylinder of mass m & radius R rolls down inclined plane without slipping. The
speed of C.M. when it reaches the bottom is
A) (2gh)1/2

B) (4gh/3)1/2
C) (3/4gh)1/2

D) (4gh)1/2
18 The least coefficient of friction for an inclined plane inclined at angle a with horizontal
in order that a solid cylinder will roll down without slipping is
A) (2/3)tanα

B) (2/7)tanα

C) tanα

D) (5/7)tanα
19 Three masses are placed on the x-axis: 300 g at origin, 500g at x=40 cmand 400g at x
=70cm. The distance of the centre of mass from the origin is
A) 40cm

B) 45cm

C) 50cm

D) 30cm
20 A body A of mass M while falling vertically downwards under gravity breaks into two
parts; f a body B of mass - M and a body C of mass - M. The canter of mass of bodies B
and C taken together shifts compared to that of body A
A) does not shift

B) depends on height of breaking

C) towards body B

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 D) towards body C
21 A symmetric lamina of mass M consists of a square shape with a semicircular
section over each of the edge of the square as shown in figure. The side of the
square is 2a. The moment of inertia of the lamina about an axis through its
centre of mass and perpendicular to the plane is 1.6Ma2. The moment of
inertia of the lamina about the tangent AB in the plane of the lamina is _____.

Ans
Hint:

22 If the mass of sun were ten times smaller and gravitational constant G were ten
times larger in magnitudes then which one is a false statement
(a) walking on ground would became more difficult.
(b) the acceleration due to gravity on earth will not change.
(c) raindrops will fall much faster.
(d) airplanes will have to travel much faster
23 A mass M is split into two parts, m and (M?m), which are then separated by a certain
distance. What ratio of m/M maximizes the gravitational force between the two parts
A) 1/3

B) 1/2

C) 1/4

D) 1/5
24 the radius and mass of earth are increased by 0.5%. Which of the following statements
are true at the surface of the earth
A) g will increase
B) g will decrease
C) Escape velocity will remain unchanged
D) Potential energy will remain unchanged

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25 A body of mass m is taken from earth surface to the height h equal to radius of earth,
the increase in potential energy will be
A) mgR

B) (1/2)mgR

C) 2 mgR

D) 14mgR
26 A satellite is launched into a circular orbit of radius R around the earth. A second
satellite is launched into an orbit of radius (1.01)R. The period of the second satellite is
larger than that of the first one by approximately
A) 0.5%

B) 1.0%

C) 1.5%

D) 3.0%
27 If the distance between the earth and the sun becomes half its present value, the
number of days in a year would have been
A) 64.5

B) 129

C) 182.5

D) 730
28 The mass of a spaceship is 1000 kg. It is to be launched from the earth’s surface out
into free space. The value of ‘g’ and ‘R’ (radius of the earth) is 10 m/s2 and 6400 km
respectively. The required energy for this work will be

(a) 6.4 x 1010 Joules

(b) 6.4 x 1011 Joules

(c) 6.4 x 108 Joules

(d) 6.4 x 109 Joules

29 The height at which the acceleration due to gravity becomes g/9 (where g = the
acceleration due to gravity on the surface of the earth) in terms of R, the radius of the
earth, is

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 (a) R/2

(b) R/3

(c) 2R

(d) 3R
30 A simple pendulum has a time period T1 when on the earth’s surface, and T2 when
taken to a height R above the earth’s surface, where R is the radius of the earth. The
value of T2/T1 is

(a) 1

(b) 3

(c) 4

(d) 2
Hint: time period =2π(L/g)1/2
31 Two particles of equal mass “m” go around a circle of radius R under the action of
their mutual gravitational attraction. The speed of each particle with respect to their
centre of mass is
(a) (Gm/R)1/2
(b) (Gm/4R)1/2
(c) (Gm/3R)1/2
(d) (Gm/2R)1/2

32
A particle is fired vertically upwards with a speed of If the radius of the earth
is R then the maximum height attainded by the particle will be:(Ve is escape velocity)
A)R
B)2 R
C)3 R
D)4 R

33 The time period of a simple pendulum at the centre of earth is:

A.zero
B.infinite
C.less than zero
D.none of these
34 A particle hanging from a massless spring stretches it by 2 cm at earth's surface. How
much will the same particle stretch the spring at height 2624 km from the surface of

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 earth ? (Radius of earth = 6400 km)
A.1 cm
B.2 cm
C.3 cm
D.4 cm

35 Three particles A,B,C each of mass m are placed at the corner of the equilateral
triangle of side a. Question 5
Find the potential energy of the system
(a) −3Gm2/a
(b) −3Gm2/2a
(c) −Gm2/3a
(d) None of these

Find the work done on this system if the side of the triangle is changed from a
to 3a
(a) 4Gm2/a
(b) 3Gm2/a
(c) Gm2/a
(d) 2Gm2/a
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