System of Particles and Rotational Motion

A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after 2 revolutions is :

1. 2 10-3 N m
2. 2 10-6 N m
3. 2 106 N m
4. 12 10-4 N m

A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it?

1. 1 J
2. 2 J
3. 3 J
4. 30 kJ

A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy (Kr) simultaneously. The ratio Kt : (Kt + Kr) for the sphere is

1. 7 : 10
2. 5 : 7
3. 10 : 7
4. 2 : 5

A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere?

1. Angular velocity
2. Moment of inertia
3. Rotational kinetic energy
4. Angular momentum

Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation

1. WC > WB > WA
2. WA > WB > WC
3. WB > WA > WC
4. WA > WC > WB

The moment of the force, F = 4 i + 5 j - 6 k at (2, 0, −3), about the point (2, −2, −2), is given by

1. -8 i - 4 j - 7 k
2. -4 i - j - 8 k
3. -7 i - 8 j - 4 k
4. -7 i - 4 j - 8 k

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 of 30 N?

1. 0.25 rad s-2
2. 25 rad s-2
3. 5 m s-2
4. 25 m s-2

Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities 1 and 2. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is

1. 14I( 1 - 2)2
2. I( 1 - 2)2
3. 18I( 1 - 2)2
4. 12I( 1 + 2)2

Which of the following statements are correct ?

1. A and B only
2. B and C only
3. C and D only
4. B and D only

A disc and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

1. Both reach at the same time
2. Depends on their masses
3. Disc
4. Sphere