Rotation of Rigid Bodies MCQ Test

Rotation of Rigid Bodies MCQ Test – 1

1. A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of an inclined plane and released. The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling. Least time will be taken in reaching the bottom by: (a)

The solid sphere

(b)

The hollow sphere

(c)

The disc

(d)

All will take same time

2. A solid homogeneous sphere is moving on a rough horizontal surface, partly rolling and partly sliding. During this king of motion of the sphere: (a)

Total KE is conserved

(b) Angular momentum of the sphere about the point of contact with the plane is conserved (c)

Only the rotational KE about centre of mass is conserved

(d)

Angular momentum about centre of mass is conserved

3. The least coefficient of friction for an inclined plane inclined at an angle  with horizontal, in order that a solid cylinder will roll down without slipping is:

(a)

(b)

(c)

(d) 4. A thin circular ring of mass M and radius R is rotating about its axis with a constant angular velocity . Two objects each of mass m are attached gently to the ring. The wheel now rotates with an angular velocity:

(a)

(b)

(c)

(d) 5. A uniform rod of mass 2 kg and length 1 m lies on a smooth horizontal plane. A particle of mass 1 kg moving at a speed of 2 m/s perpendicular to the length of the rod

strikes it at a distance m from the centre and stops. What is angular velocity of the rod about its centre just after the collision:

(a)

3 rad/s

(b)

4 rad/s

(c)

1 rad/s

(d)

2 rad/s

6. A particle of mass 5 g is moving with a uniform speed of

along the line in –cm2/s is: (a)

Zero

(b)

30

cm/s is the xy-plane

cm. The magnitude of its angular momentum about the origin

(c)

(d)

7. The ratio of the time taken by a solid sphere and that taken by a disc of the same mass and radius to roll down a rough inclined plane from rest, from the same height is: (a)

15 : 14

(b) (c)

14 : 15

(d)

8. A solid cylinder and a solid sphere, both having the same mass and radius, are released from a rough inclined plane. Both roll without slipping. Then :

(a)

The force of friction that acts on the two is the same

(b)

The force of friction is greater in case of sphere than for a cylinder

(c)

The force of friction is greater in case of a cylinder than for a sphere

(d) The force of friction will depend on the nature of the surface of the body that is moving and that of the inclined surface, and is independent of the shape and size of the moving body

9. A uniform metre stick of mass M is hinged at one and, supported in horizontal direction by a string attached to the other end. What would be the initial acceleration of the centre of the stick if the string is cut.

(a) (b)

g

(c) (d)

4g

10. The speed of homogeneous solid sphere after rolling down an inclined plane of vertical height h, from rest without sliding is:

(a)

(b)

(c)

(d) 11. A rectangular block with a square shape base (a  (a)) and height h moves on a horizontal surface by a force F at top of the cube in a direction perpendicular to one of the edges. If be the coefficient of friction, the block will topple before it slides if:

(a)

(b)

>

(c)

(d)

12. A plank of mass M is placed over smooth inclined plane and a sphere is also placed over the plank. Friction is sufficient between sphere and plank. If plank and sphere are released from rest. The frictional force on sphere is: (a)

Up the plane

(b)

Down the plane

(c)

Zero

(d)

Horizontal

13. A circular disc of mass m and radium R rests flat on a horizontal frictionless surface. A bullet, also of mass m, and moving with a velocity v, strikes the disc and gets embedded in it. The angular velocity with which the system rotates after the bullet strikes the hoop is:

(a)

(b)

(c)

(d) Answer Keys: 1.

d

2.

b

3.

c

4.

c 5.

6.

d

7.

b

8.

c

9.

c 10.

11.

d

12.

c 13.

a

d d