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Moment of inertia / p.1
1.
(91-I-9)
3.
The turntable of a gramophone rotates at a steady
angular speed
(92-I-7)
A gymnast on a trampoline is performing a
 . A record is dropped from rest
somersault and draws his knees to his chest. Which
on the turntable. Initially, the record slips but it
of the following quantities (about a horizontal axis
undergoes uniform angular acceleration and
through his centre of mass) will be increased?
eventually moves with the same angular speed as
the turntable. The turntable turns through an angle
(1)
His angular momentum.

while the record is slipping on its surface. Find
(2)
His moment of inertia.
the angular acceleration of the record and the angle
(3)
His rotation speed.
which it turns through before it attains the steady
speed of the turntable.
Angular acceleration
A.
 2 /( 2 )
 /2
B.
 2 /( 2 )

C.
 2 /( 2 )
2
 2 /
 2 /
 /2

D.
E.
2.
Angle
(92-I-6)
4.
A.
(1), (2) and (3)
B.
(1) and (2) only
C.
(2) and (3) only
D.
(1) only
E.
(3) only
(93-I-2)
A sphere of mass 1 kg is released from rest on an
inclined plane of inclination 30o to the horizontal
(as shown). If the sphere rolls without slipping,
find the gain in kinetic energy and the work done
against friction by the sphere after travelling a
distance of 5 m along the plane.
Two objects are moving with instantaneous
gain in kinetic
work done against
velocities as shown in the above diagram. The total
energy/J
friction/J
angular momentum about the point O at this instant
is
A.
25
0
25
B.
25
2 -1
C.
50
B.
2 -1
6 kg m s
D.
50
0
C.
2
-1
E.
50
25
2
-1
A.
4 kg m s
10 kg m s
D.
20 kg m s
E.
30 kg m2 s-1
cannot be determined
Moment of inertia / p.2
5.
(93-I-5)
7.
(94-IIA-3)
The above diagram shows a uniform hollow metal
sphere with a small opening on top. O is the
A uniform metre rule of mass 0.15 kg is hinged to a
position of the centre of mass of the hollow sphere.
wall at P and the other end R is connected by a wire
What will happen to the position of the centre of
attached to the wall at Q, vertically above P. A block
mass of the system as the sphere is being slowly
X of mass 0.1 kg is hung from the rule 30 cm from R.
filled with oil from the opening?
The metre rule is horizontal. Find the moment about
P produced by the tension in the wire.
A.
B.
C.
D.
It will fall gradually, and its final
position will be below O.
A.
1.45 Nm
It will fall gradually at first and then
B.
1.05 Nm
rise to its original position.
C.
0.75 Nm
It will rise gradually and its final
D.
0.70 Nm
position will be above O.
E.
0.25 Nm
It will rise gradually at first and then
fall to its original position.
E.
It will remain unchanged throughout
the process.
6.
(93-I-9)
A ring of radius a is made from thin wire. The
moment of inertia of the ring about an axis through
its centre and perpendicular to its plane is I. What
would be the moment of inertia of a ring, made
from the same type of wire but with radius 2a,
about a similar axis?
A.
I
B.
2I
C.
4I
D.
8I
E.
16I
Moment of inertia / p.3
8.
(94-IIA-10)
The above figure shows a uniform ring and a
10.
A.
1.0 m
B.
1.5 m
C.
1.8 m
D.
2.1 m
E.
2.4 m
(95-IIA-8)
uniform disc, with equal mass and radius,
smoothly hinged at points
O and O on their
respective circumferences. They are set into small
oscillation of equal amplitude about axes through
O and O perpendicular to the plane of the
paper. Which of the following statements is/are
correct?
The figure shows a uniform rigid beam AB,
(1)
The moment of inertia of the ring about the
pivoted at A, held in horizontal position by a wire
O is greater than that of the
disc about the axis through O .
attached to a wall at point C, vertically above A.
(2)
The period of oscillation of the ring is longer.
gradually from A towards B, which of the
(3)
Both the ring and the disc have the same
following quantities will increase?
axis through
The beam carries a load W. If W is shifted
total kinetic energy when their centres are
vertically below their respective axes.
9.
(1)
The tension in the wire.
(2)
The horizontal compression force in the
A.
(1) only
beam.
B.
(3) only
C.
(1) and (2) only
D.
(2) and (3) only
A.
(1) only
E.
(1), (2) and (3)
B.
(3) only
C.
(1) and (2) only
D.
(2) and (3) only
E.
(1), (2) and (3)
(3)
(95-IIA-4)
For safety reasons, a vehicle should be so designed
that no sideways toppling occurs before reaching
o
an angle of inclination of 30 . If the centre of
gravity of that vehicle is 1.8 m above the ground,
what is the minimum separation x between its
wheels?
The vertical component of the reaction at A.
Moment of inertia / p.4
11.
(95-IIA-9)
13.
(97-IIA-7)
A constant external torque X is applied to a
flywheel which is initially at rest. The angular
speed of the flywheel increases to a certain value
after 21 s. If the external torque is now doubled,
the flywheel will acquire the same angular speed
Point masses of 2 kg and 4 kg are attached to the
after 9 s. Find the average frictional torque exerted
ends of an L-shaped light frame ABC, with AB
at the bearings of the flywheel.
vertical and BC horizontal. The frame is pivoted at
and free to rotate about point B in a vertical plane.
A.
What is the initial angular acceleration of the
system when released from rest?
A.
4.4 rad s-2
B.
5.0 rad s-2
C.
5.6 rad s-2
D.
8.0 rad s-2
E.
10.0 rad s-2
B.
C.
D.
E.
1
X
2
3
X
7
7
X
10
4
X
7
1
X
4
12. (96-IIA-8)
Three uniform wires, of same length and mass but
14. (98-IIA-7)
with different shapes, are hinged to an axis passing
Two small identical coins A and B are placed on a
through O and perpendicular to the plane of the
horizontal turntable which is kept rotating at a
paper as shown. Arrange their moments of inertia
constant angular speed about a vertical axis through
about O in ascending order of magnitude.
its centre. The distance of B from the axis of rotation
is twice that of A from the axis. Which of the
following statements is/are correct?
(1) The kinetic energy of B is four times that of A.
(2) The frictional force acting on B is double that
acting on A.
(3) If the angular speed of the turntable gradually
A.
(1), (2), (3)
increases, B will slip before A.
B.
(2), (1), (3)
C.
(1), (3), (2)
A. (1) only
D.
(2), (3), (1)
B.
(3) only
E.
(3), (2), (1)
C.
(1) and (2) only
D. (2) and (3) only
E.
(1), (2) and (3)
Moment of inertia / p.5
15.
(99-IIA-6)
17.
(00-IIA-3)
A light rigid rod PQ is hinged smoothly to the wall
A light, rigid rod of length 1 m is hinged smoothly
at one end while the other end is connected by an
at P at one end. Two small masses m and 2m are
inextensible string to a point R directly above P.
fixed to the mid-point and the other end of the rod
A weight W is suspended from a point on the rod.
respectively. The rod is held vertically above P and
If the rod remains horizontal, which of the
is released from rest. What is the total rotational
following change(s) would increase the tension in
energy of the system when the rod rotates to the
the string?
position vertically below P? (Neglect air
resistance)
(1)
Shifting the weight towards Q
(2)
Replacing the string with a shorter one and
A.
2.5 mg
connecting it to the mid-points of PQ and PR
B.
4.5 mg
C.
5 mg
connecting it to a point higher than R
D.
7.5 mg
A. (1) only
E.
9 mg
B. (3) only
(3)
Replacing the string with a longer one and
C. (1) and (2) only
16.
(99-IIA-7)
D. (2) and (3) only
E. (1), (2) and (3)
18.
(00-IIA-14)
With his arms and legs outstretched, a diver leaves
a high-diving board with some initial angular
A turntable of moment of inertia 1.0  10
3
kg m
2
velocity. Before he enters the water, which of the
is under the action of a torque. The variation of the
following statements is INCORRECT? (Neglect
torque  acting about the axis of rotation with time
air resistance.)
t is as shown. If the turntable is at rest initially,
what is its angular momentum at t = 20 s?
A.
His angular momentum about the
center of gravity remains constant.
2
1
A.
40 kg m s
B.
2
1
2
1
C.
D.
E.
100 kg m s
200 kg m s
5
2
B.
No external force acts on him.
C.
His loss in potential energy becomes
his kinetic energy.
1
1 10 kg m s
2  10 5 kg m 2 s 1
D.
He can decrease his moment of inertia
by pulling his arms and legs to his
chest.
E.
He can make more turns before
reaching the water surface by coiling
up his body.
Moment of inertia / p.6
19.
(01-IIA-4)
21.
Which of the following is/are vector quantities?
(02-IIA-11)
A thin uniform rod of mass 0.1 kg and length 0.3 m
is smoothly hinged at its lower end as shown. It is
20.
(1) impulse
then released from rest from the vertical position.
(2) moment of inertia
What is its angular speed, in radian per second,
(3) pressure
when it becomes horizontal? (Moment of inertia of
the rod about one end is
3  10 3 kg m 2 )
A.
(1) only
B.
(3) only
C.
(1) and (2) only
A.
6.3
D.
(2) and (3) only
B.
10
E.
(1) ,(2) and (3)
C.
14
D.
50
(01-IIA-9)
A solid cylinder and a hollow cylinder, each having
22.
(04-IIA-8)
the same mass and external radius, are released
Long ago, astronomers wanted to find out whether
together from rest, side by side, at the top of a
the ring of Saturn is a rigid body or a group of
rough inclined plane. Both cylinders roll down the
satellites revolving around Saturn. The linear
inclined plane without slipping. Which of the
speeds v of different layers of the ring were
following statements is INCORRECT?
measured and how v varies with the distance r
from the centre of Saturn was determined. Which
A. The solid cylinder has a smaller moment of
inertia about its axis.
B. The solid cylinder reaches the bottom of the
incline first.
C. There is no work done by each cylinder
against the friction due to the incline.
D. The total kinetic energy of each cylinder is the
same at the bottom of the incline.
of the following relations between v and r
supports the suggestion that
(1) the ring is a rigid body,
(2) the ring is a group of satellites
revolving around Saturn
(1)
(2)
1
A.
v r
v
r
E. The solid cylinder has greater rotational
kinetic energy at the bottom of the incline.
B.
v r
C.
v r
D.
v r
v
v
v
1
r
1
r
1
r