A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force 30 N?

(a)

0.25 rad s^-2

(b)

25 rad s^-2

(c)

5 ms^-2 

(d)

25 ms^-2

A rigid body rotates with an angular momentum L. If its kinetic energy is halved, the angular momentum becomes,

(a)

L

(b)

L/2

(c)

2L

(d)

L/\(\sqrt{2}\)

From a disc of radius R a mass M, a circular hole of diameter R, whose rim passes through the center is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis passing through it

(a)

15MR²/32

(b)

13MR²/32

(c)

11MR²/32

(d)

9MR²/32

The speed of the center of a wheel rolling on a horizontal surface is v_o.  A point on the rim in level with the center will be moving at a speed of,

(a)

zero

(b)

v_o

(c)

\(\sqrt{2}\)v_o

(d)

2v_o

A round object of mass M and radius R rolls down without slipping along an inclined plane. The fractional force, 

(a)

dissipates kinetic energy as heat

(b)

decreases the rotational motion

(c)

decreases the rotational and transnational motion

(d)

converts transnational energy into rotational energy

Where will be the centre of mass on combining two masses m and M (M > m)?

(a)

Towards m

(b)

Towards M

(c)

Between m & M

(d)

away from m & M

Moment of force is called _______________.

(a)

angular momentum

(b)

torque

(c)

couple

(d)

none

If there is change of angular momentum from J to 4J in 4S, then the torque is _____________.

(a)

3/4 J

(b)

1J

(c)

5/4 J

(d)

4/3 J

If a solid sphere and solid cylinder of same mass and radius rotate about their own axis the M.I. will be greater for _______________.

(a)

Solid sphere

(b)

Solid cylinder

(c)

Both (a) and (b) 

(d)

Equal both

A particle undergoes uniform circular motion. About which point on 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

How will you find the direction of rotation using the direction of torque?

What is the effect of Torque on Rigid Bodies.

When a tree is cut, the cut is made on the side facing the direction in which the tree is required to fall. Why?

Give an example to show that the following statement is false. 'any two forces acting on a body can be combined into single force that would have same effect'.

A solid sphere of mass 20 kg and radius 0.25 m rotates about an axis passing through the center. What is the angular momentum if the angular velocity is 5 rad s^-1.

Define centre of mass.

How do you distinguish between stable and unstable equilibrium?

Mention any two physical significance of moment of inertia?

Find the expression for radius of gyration?

Derive an expression for work done by Torque?

Derive the expression for moment of inertia of a rod about its center and perpendicular to the rod?

Derive the expression for moment of inertia of a uniform disc about an axis passing through the center and perpendicular to the plane.

Write an expression for the kinetic energy of a body in pure rolling.