1. No category

R. K. Academy Lonawala JEE -2014
Physics : Rotational Motion
Example 1:
Example 2:
Example 3:
Example 4:
Example 5:
Five particles of mass = 2 kg are attached to the rim of a circular disc of radius 0.1 m and negligible mass.
Moment of inertia of the system about the axis passing through the centre of the disc and perpendicular to
its plane is
[BHU 2003]
(a) 1 kg m2
(b) 0.1 kg m2
(c) 2 kg m2
(d) 0.2 kg m2
A circular disc X of radius R is made from an iron plate of thickness t, and another disc Y of radius 4R is
t
made from an iron plate of thickness . Then the relation between the moment of inertia IX and IY is
4
(a) IY = 64IX
(b) IY = 32IX
(c) IY = 16IX
(d) IY = IX
Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis
perpendicular to its plane and passing through a point on its rim will be
[UPSEAT 2002]
(a) 5 I
(b) 6 I
(c) 3 I
(d) 4 I
Four thin rods of same mass M and same length l, form a square as shown in figure. Moment of inertia of
this system about an axis through centre O and perpendicular to its plane is
[MP PMT 2002]
(a)
4
Ml 2
3
(b)
Ml 2
3
(c)
Ml 2
6
(d)
2
Ml 2
3
l
A
B
P
l
l
O
D
C
l
Three rings each of mass M and radius R are arranged as shown in the figure. The moment of inertia of
the system about YY will be
Y
Example 6:
3
1
(a) 3 MR2
(b)
MR 2
2
3
2
7
2
Y
(c) 5 MR2
(d)
MR
2

Let l be the moment of inertia of an 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) l
Example 7:
(b) l sin2 
(c) l cos 2 
(d) l cos 2

2
Three rods each of length L and mass M are placed along X, Y and Z-axes in such a way that one end of
each of the rod is at the origin. The moment of inertia of this system about Z axis is
5 ML2
4 ML2
ML2
2 ML 2
(b)
(c)
(d)
3
3
3
3
Three point masses each of mass m are placed at the corners of an equilateral triangle of side a. Then the
moment of inertia of this system about an axis passing along one side of the triangle is
[AIIMS 1995]
(a)
Example 8:
(a) ma 2
Example 9:
(b) 3ma 2
(c)
3
ma 2
4
(d)
2
ma 2
3
Two identical rods each of mass M. and length l are joined in crossed position as shown in figure. The
moment of inertia of this system about a bisector would be
(a)
Ml 2
6
(b)
Ml 2
12
(c)
Ml 2
3
(d)
Ml 2
4
B1
B2
Example 10:
The moment of inertia of a rod of length l about an axis passing through its centre of mass and
perpendicular to rod is I. The moment of inertia of hexagonal shape formed by six such rods, about an
axis passing through its centre of mass and perpendicular to its plane will be
(a) 16I
Example 11:
(c) 60 I
(d) 80 I
A horizontal heavy uniform bar of weight W is supported at its ends by two men. At the instant, one of the
men lets go off his end of the rod, the other feels the force on his hand changed to
(a) W
Example 12:
(b) 40 I
(b)
W
2
(c)
3W
4
(d)
W
4
Consider a body, shown in figure, consisting of two identical balls, each of mass M connected by a light
rigid rod. If an impulse J = Mv is imparted to the body at one of its ends, what would be its angular
velocity
L
(a) v/L
M
(b) 2v/L
M
J = Mv
(c) v/3L
(d) v/4L
Example 13:
Example 14:
A thin circular ring of mass M and radius R is rotating about its axis with a constant angular velocity .
Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the
ring. The angular velocity of the ring will be
[CBSE PMT 2003]
M
(M  4 m )
(M  4 m )
M
(a)
(b)
(c)
(d)
M  4m
M  4m
4m
M
A ring of radius 0.5 m and mass 10 kg is rotating about its diameter with an angular velocity of 20 rad/s.
Its kinetic energy is
[MP PET 2003]
(a)
Example 15:
Example 16:
Example 17:
An automobile engine develops 100 kW when rotating at a speed of 1800 rev/min. What torque does it
deliver
[CBSE PMT 2000]
(a) 350 N-m
(b) 440 N-m
(c) 531 N-m
(d) 628 N-m
A disc and a ring of same mass are rolling and if their kinetic energies are equal, then the ratio of their
velocities will be
(a) 4 : 3
(b) 3 : 4
(c) 3 : 2
(d) 2 : 3
If the angular momentum of a rotating body is increased by 200%, then its kinetic energy of rotation will
be increased by
(a) 400%
(b) 800%
(c) 200%
(d) 100%
Example 18:
A flywheel of moment of inertia 0.32 kg-m2 is rotated steadily at 120 rad / sec by a 50 W electric motor.
The kinetic energy of the flywheel is
(a) 4608 J
(b) 1152 J
(c) 2304 J
(d) 6912 J
Example 19:
A sphere rolls down on an inclined plane of inclination . What is the acceleration as the sphere reaches
bottom
[Orissa JEE 2003]
5
2
3
2
(a)
(b)
(c)
(d) g sin 
g sin 
g sin 
g sin 
5
5
7
7
A thin uniform circular ring is rolling down an inclined plane of inclination 30° without slipping. Its linear
acceleration along the inclined plane will be
[CBSE PMT 1992; BHU 1998]
(a) g 2
(b) g 3
(c) g 4
(d) 2g 3
Example 20:
Example 21:
A solid sphere of mass 0 .1 kg and radius 2 cm rolls down an inclined plane 1.4 m in length (slope 1 in
10). Starting from rest its final velocity will be
(a) 1.4 m / sec
(b) 0.14 m / sec
(c) 14 m / sec
(d) 0.7 m / sec
Example 22:
A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and
moment of inertia about it is I. A weight mg is attached to the end of the cord and falls from rest. After
falling through a distance h, the angular velocity of the wheel will be
(a)
2 gh
I  mr
(b)
2mgh
I  mr
2
(c)
2mgh
I  2mr 2
(d)
2 gh