ROTATION
Rotation
Level - 1
1. A disc is rotating with angular velocity . If a 6. A disc is rotating with angular velocity about
child sits on it, what is conserved? its axis. A force F acts at a point whose
position vector with respect to the axis of
(a) Linear momentum
rotation is r . The power associated with the
(b) Angular momentum torque due to the force is given by
(c) Kinetic energy (a) (r F ). (b) (r F )
(d) Moment of inertia (c) r . (F ) (d) r (F )
2. When a mass is rotating in a plane about a fixed 7. The moment of inertia of a solid sphere of
point, its angular momentum is directed along mass M and radius R about a tangent to the
sphere is
(a) A line perpendicular to the plane of rotation
2 6
(b) The line making an angle of 45° to the (a) MR 2 (b) MR 2
5 5
plane of rotation
4 7
(c) MR 2 (d) MR 2
(c) The radius 5 5
(d) The tangent to the orbit 8. The moment of inertia of a body depends upon
3. Which of the following is the correct (a) Mass of the body
relation between linear velocity v and angular (b) Axis of rotation of the body
velocity of a particle? (c) Shape and size of the body
(a) v r (b) v r (d) All of these
(c) r v (d) v r 9. Two masses each of mass M are attached to
the end of a rigid massless rod of length L. The
4. A body is rotating with angular velocity moment of inertia of the system about an axis
(3iˆ 4 jˆ kˆ ) . The linear velocity of a point passing centre of mass and perpendicular to its
length is
having position vector r (5iˆ 6 jˆ 6kˆ ) is
ML2 ML2
(a) 6iˆ 2 jˆ 3kˆ (b) 18iˆ 3 jˆ 2kˆ (a) (b)
4 2
(c) 18iˆ 13 jˆ 2kˆ (d) 6iˆ 2 jˆ 8kˆ (c) ML2 (d) 2ML2
10. The radius of gyration of an uniform rod of
5. The force 7iˆ 3 jˆ 5kˆ acts on a particle whose
length about an axis passing through one of
position vector is iˆ jˆ kˆ . What is the torque its ends and perpendicular to its length is
of a given force about the origin?
(a) (b)
2 3
(a) 2iˆ 12 jˆ 10kˆ (b) 2iˆ 10 jˆ 12kˆ
2
(c) (d)
(c) 2iˆ 10 jˆ 10kˆ (d) 10iˆ 2 jˆ kˆ
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3 2
Rotation
Level - 1
11. Four particles each of mass m are kept at the 15. Three identical spherical shells, each of
four corners of a square of edge a. Find the mass m and radius r are placed as shown in
moment of inertia of the system about a line
figure. Consider an axis XX , which is touching
perpendicular to the plane of the square and X
to two shells and passing
passing through the centre of the square.
through diameter of third shell.
2
(a) 2ma m m
Moment of inertia of the
2
(b) 3ma system consisting of these
three spherical shells about X
(c) 4ma 2
XX axis is
(d) 1ma 2 m m
11 2
12. Four point masses are connected by a (a) mr (b) 3 mr 2
5
massless rod as shown in figure. Find out the
moment of inertia of the system about axis CD? 16 2
(c) mr (d) 4 mr 2
5
(a) 5ma 2
C 16. Four identical thin rods each of mass M and
2
(b) 15ma m 2m 3m 4m length , form a square frame. Moment of
inertia of this frame about an axis through the
(c) 10ma 2 a a a
D centre of the square and perpendicular to its
2
(d) 20ma plane is
13. Four point masses each of mass m kept at the 4 2
(a) M 2 (b) M 2
four corners of a square of side length ‘a’ find 3 3
the moment of system inertia about axis CD.
13 1
(c) M 2 (d) M 2
3 3
(a) 3ma 2 a
D
a a 17. The ratio of the radii of gyration of a circular disc
2
(b) 2ma
45° to that of a circular ring, each of same mass and
a
radius, around their respective axes is
(c) 5ma 2
(a) 3: 2 (b) 1: 2
(d) 4ma 2 C
(c) 2 :1 (d) 2: 3
14. Calculate the moment of inertia of a ring having
mass M, radius R and having uniform mass 18. The moment of inertia of a uniform circular disc
distribution about an axis passing through the of radius R and mass M about an axis passing
centre of ring and perpendicular to the plane of
from the edge of the disc and normal to the disc
ring?
is
R
dm
axis
1
(a) MR 2 (b) MR 2
2
(a) 1 MR 2 (b) 3 MR 2
3
7 3
(c) MR 2 (d) MR 2
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2 2
(c) 2 MR (d) MR 2 2
Rotation
Level - 1
19. The moment of inertia of a disc of mass M and 25. A grindstone has a moment of inertia of
radius R about a tangent to its rim in its plane is
6 kg m2 . A constant torque is applied and the
2 3
(a) MR 2 (b) MR 2 grindstone is found to have a speed of 150 rpm,
3 2
10 seconds after starting from rest. The torque
4 5
(c) MR 2 (d) MR 2
5 4 is
20. In a rectangle ABCD(BC = 2AB). The moment (a) 3 Nm (b) 3 Nm
of inertia is minimum along axis through
(a) BC
F
(c) Nm (d) 4 Nm
A D 3
(b) BD
E G 26. The instantaneous angular position of a point
(c) HF
B C
H on a rotating wheel is given by the equation
(d) EG
21. If a flywheel makes 120 rev/min, then its (t ) 2t 3 6t 2 . The torque on the wheel
angular speed will be becomes zero at
(a) 8 rad/s (b) 6 rad/s
(a) t 1 s (b) t 0.5 s
(c) 4 rad/s (d) 2 rad/s
(c) t 0.25 s (d) t 2 s
22. A thin uniform circular ring is rolling down an
inclined plane of inclination 30° without slipping. 27. A solid cylinder of mass 20 kg and radius 20 cm
Its linear acceleration along the inclined plane
rotates about its axis with a angular speed
will be
100 rad s 1 . The angular momentum of the
g g
(a) (b)
2 3 cylinder about its axis is
g 2g (a) 40 J s (b) 400 J s
(c) (d)
4 3
(c) 20 J s (d) 200 J s
23. Moment of inertia of a uniform circular disc
about a diameter is . Its moment of inertia 28. A child is standing with his two arms
about an axis perpendicular to its plane and
outstretched at the centre of a turntable that is
passing through a point on its rim will be
rotating about its central axis with an angular
(a) 5 (b) 3
speed 0 . Now, the child folds his hands back
(c) 6 (d) 4
so that moment of inertia becomes 3 times the
24. The angular speed of a motor wheel is
increased from 1200 rpm to 3120 rpm in 16 initial value. The new angular speed is
seconds. The angular acceleration of the motor
0
wheel is (a) 30 (b)
3
(a) 2 rad s 2 (b) 4 rad s 2
0
(c) 60 (d)
4
(c) 6 rad s 2 (d) 8 rad s 2 6
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Rotation
Level - 1
29. Find moment of inertia about centroidal axis of 32. A wheel of radius r rolls (rolling without
a bobbin, which is constructed by joining sleeping) on a level road as shown in figure.
coaxially two identical discs each of mass m Find out velocity of point A and B.
and radius 2r to a cylinder of mass m and
(a) 1 v B
radius r as shown in the figure.
(b) 3 v r
v
Centroidal
axis (c) 4 v A
(d) 2 v
9 2 7 2 33. Find the minimum value of F to topple about an
(a) mr (b) mr
2 2 edge. a
F
3 2 7 2 b M
(c) mr (d) mr
7 3
30. Find the torque of weight about the axis passing
Mga Mga
through point P. (a) (b)
b 2b
(a) 4mgR sin
R 2Mga Mga
(c) (d)
(b) 3mgR sin m 3b 3b
(c) mgR sin P 34. A thin meter scale is kept vertical by placing its
one end on floor, keeping the end in contact
(d) 2mgR sin
stationary, it is allowed to fall. Calculate the
31. A uniform rod of length , mass m is hung from velocity of its upper end when it hit the floor.
two strings of equal length from a ceiling as
(a) 3g (b) 2g
shown in figure. Determine the tensions in the
strings? (c) g (d) 4g
(a) 1 mg/3
(b) 2 mg/3
(c) 3 mg/3
A B
(d) 4 mg/3
5
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