Rotational Motion MCQ
Rotational Motion MCQ
Rotational Motion MCQ
r , and
be the torque
of this force about the origin. Then
( a )
. r = 0 and
. F = 0 ( b )
. r = 0 and
. F 0
( c )
. r 0 and
. F = 0 ( d )
. r 0 and
. F 0 [ AIEEE 2003 ]
8 ) A circular disc X of radius R is made from an iron plate of thickness t, and another
disc Y of radius 4R is made from an iron plate of thickness t / 4. The relation between
the moments of inertia
x
and
y
is
( a )
y
= 64
x
( b )
y
= 32
x
( c )
y
= 16
x
( d )
y
=
x
[ AIEEE 2003 ]
9 ) The moment of inertia of a rigid body depends upon
( a ) mass of the body ( b ) angular acceleration of the body
( c ) angular velocity of the body ( d ) distribution of mass from the axis of rotation
[ AIEEE 2002 ]
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06 - ROTATIONAL MOTION Page 2
( Answers at the end of all questions )
10 ) If moment of inertia of a wheel, having radius of gyration 60 cm, is 360 kg-m
2
, then
mass of the wheel is
( a ) 200 kg ( b ) 500 kg ( c ) 800 kg ( d ) 1000 kg [ AIEEE 2002 ]
11 ) A particle moves on a circular path with decreasing speed. Choose the correct
statement.
( a ) Angular momentum remains constant. ( b ) Acceleration is towards the centre.
( c ) Particle moves on a spiral path with decreasing radius.
( d ) The direction of angular momentum remains constant. [ IIT 2005 ]
12 ) Mass and radius of a circular disc is 9M and R respectively. Moment of inertia of the
disc about an axis passing through point O and perpendicular to its plane after removal
of a disc of radius R / 3 touching its circumference is
( a )
2
MR
9
37
( b )
2
MR 9 ( c )
2
MR
9
40
( d )
2
MR 4 [ IIT 2005 ]
13 ) A disc is rolling ( without slipping ) on a horizontal surface. C is
the centre and P and Q are two particles of the disc equidistant
from C. Let V
P
, V
Q
and V
C
be the magnitudes of velocities of
the particles P and Q and the particle at C respectively. Then
( a ) V
Q
> V
C
> V
P
( b ) V
Q
< V
C
< V
P
( c ) V
Q
= V
P
, V
C
= 0.5 V
P
( d ) V
Q
< V
C
> V
P
[ IIT 2004 ]
14 ) A child is standing with folded hands at the centre of a platform rotating about its
central axis. The kinetic energy of the system is K. The child now stretches his arms so
that the moment of inertia of the system doubles. The kinetic energy of the system now
is
( a ) 2 K ( b ) K / 2 ( c ) K / 4 ( d ) 4 K [ IIT 2004 ]
15 ) Two identical bodies of mass m are connected by a light rod of length l and placed
on horizontal smooth surface. An impulse mv is given at one end perpendicular to the
length of the rod. The angular velocity of the system is
( a ) v / l ( b ) 2v / l ( c ) v / 3l ( d ) v / 4l [ IIT 2003 ]
16 ) A particle undergoes uniform circular motion. About which point on the plane of the
circle, will the angular momentum of the particle remain conserved ?
( a ) centre of the circle ( b ) on the circumference of the circle
( c ) inside the circle ( d ) outside the circle [ IIT 2003 ]
17 ) Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass
and placed on a frictionalless 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 [ IIT 2002 ]
18 ) A cylinder rolls up an inclined plane, reaches some height, and then rolls down ( without
slipping throughout these motions ). The directions of the frictional force acting on the
cylinder are
( a ) up the incline while ascending and down the incline while descending
( b ) up the incline while ascending as well as descending
( c ) down the incline while ascending and up the incline while descending
( d ) down the incline while ascending as well as descending [ IIT 2002 ]
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( Answers at the end of all questions )
19 ) A circular platform is free to rotate in a horizontal plane about a vertical axis passing
through its centre. A tortoise is sitting at the edge of the platform. Now the platform is
given an angular velocity
0
. When the tortoise moves along a chord of the platform
with a constant velocity ( with respect to the platform ), the angular velocity of the
platform
t
will vary with time as
[ IIT 2002 ]
20 ) One quarter section is cut from a uniform circular disc of radius R. This
section has a mass M. It is made to rotate about a line perpendicular to
its plane and passing through the centre of the original disc. Its moment
of inertia about the axis of rotation is
( a )
2
MR
2
1
( b )
2
MR
4
1
( c )
2
MR
8
1
( d )
2
MR 2
[ IIT 2001 ]
21 ) A small block is shot into each of the four tracks as shown below. Each of the track
rises to the same height. The speed with which the block enters the track is the same
in all cases. At the highest point of the track, the normal reaction is maximum in
[ IIT 2001 ]
22 ) An equilateral triangle ABC formed from a vertical wire has two
small identical beads initially located at A. The triangle is set
rotating about the vertical axis AO. Then the beads are released
from rest simultaneously and allowed to slide down; one along AB
and the other along AC as shown. Neglecting frictional effects, the
quantities that are conserved as beads slide down are
( a ) angular velocity and total energy ( kinetic and potential )
( b ) total angular momentum and total energy
( c ) angular velocity and moment of inertia about the axis of
rotation
( d ) total angular momentum and moment of inertia about the
axis of rotation [ IIT 2000 ]
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( Answers at the end of all questions )
23 ) A long horizontal rod has a bead which can slide along its length and is initially placed
at a distance L from one end A of the rod. The rod is set in angular motion about A
with a constant angular acceleration, . If the coefficient of friction between the rod and
the bead is , and gravity is neglected, then the time after which the bead starts
slipping is
( a )
( b )
( c )
1
( d ) infinitesimal [ IIT 2000 ]
24 ) A cubical block of side L rests on a rough horizontal surface
with coefficient of friction . A horizontal force F is applied on
the block as shown. If the coefficient of friction is sufficiently
high so that the block does not slide before toppling, the
minimum force required to topple the block is
( a ) infinitesimal ( b )
4
mg
( c )
2
mg
( d ) mg ( 1 - )
[ IIT 2000 ]
25 ) A thin wire of length L and uniform linear mass density
is bent into a circular loop with centre at O as shown. The
moment of inertia of the loop about the axis XX is
( a )
2
8
L
3
( b )
2
16
L
3
( c )
2
16
L 5
3
( d )
2
8
L 3
3
[ IIT 2000 ]
26 ) A cubical block of side a is moving with velocity V on a
horizontal smooth plane as shown. It has a ridge at point O.
The angular speed of the block after it hits O is
( a )
a 4
V 3
( b )
a 2
V 3
( c )
a
V
2
3
( d ) zero [ IIT 1999 ]
27 ) A smooth sphere A is moving on a frictionless horizontal plane with angular velocity
and centre of mass velocity v. It collides elastically and head on with an identical
sphere B at rest. Neglect friction everywhere. After the collision, their angular speeds
are
A
and
B
respectively. Then
( a )
A
<
B
( b )
A
=
B
( c )
A
= ( d )
B
= [ IIT 1999 ]
28 ) A disc of mass M and radius R is rolling with angular speed
on a horizontal plane as shown. The magnitude of angular
momentum of the disc about the origin O is
( a ) MR
2
1
2
|
.
|
\
|
( b ) MR
2
( c ) MR
2
3
2
|
.
|
\
|
( d ) MR 2
2
[ IIT 1999 ]
29 ) Let I be the moment of inertia of a uniform square plate about an axis AB that passes
through its centre and is parallel to two of its sides. CD is a line in the plane of the
plate that passes through the centre of the plate and makes an angle with AB. The
moment of inertia of the plate about the axis CD is then equal to
( a ) I ( b ) I sin
2
( c ) I cos
2
( d ) I cos
2
( / 2 ) [ IIT 1998 ]
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06 - ROTATIONAL MOTION Page 5
( Answers at the end of all questions )
30 ) The torque
is perpendicular to
L in the direction of
+
( b )
2
2 1
2 1
r
M M
M M
(
+
( c )
2
2 1
2 1
r
M M
M M
(
+
-
( d )
2
2 1
2 1
r
M M
M M
(
+
-
44 ) A particle of mass m = 5 is moving with a uniform speed v = 5 2 in the XOY plane
along the line y = x + 4. The magnitude of the angular momentum about the origin is
( a ) 40 units ( b ) 60 units ( c ) 80 units ( d ) 100 units
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06 - ROTATIONAL MOTION Page 7
( Answers at the end of all questions )
45 ) A solid cylinder first rolls without sliding and then slides without rolling down the same
inclined plane. The ratio of velocities in the two cases, at the bottom of the plane is
( a ) 1 : 2 ( b ) 1 : 3 ( c ) 6 : 3 ( d ) 3 : 1
Answers
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
a c d b c b a a d d d d a b a a c b c a a b
23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
a c d a c c a a,b,c b c a,b a a,c,d b,d a b a b b b a
44 45
d c
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