System of Particles and Rotational Motion

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

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

1. 11MR232
2. 9MR232
3. 15MR232
4. 13MR232

A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of 2.0 rad s-2. Its net acceleration in m s-2 at the end of 2.0 s is approximately

1. 6.0
2. 3.0
3. 8.0
4. 7.0

Two rotating bodies A and B of masses m and 2m with moments of inertia IA and IB (IB > IA) have equal kinetic energy of rotation. If LA and LB be their angular momenta respectively, then

1. LA = LB2
2. LA = 2LB
3. LB > LA
4. LA > LB

A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation (Esphere/Ecylinder) will be

1. 2 : 3
2. 1 : 5
3. 1 : 4
4. 3 : 1

A light rod of length l has two masses m1 and m2 attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is

1. m1m2m1+m2l2
2. m1+m2m1m2l2
3. (m1+m2)l2
4. m1m2 l2

Point masses m1 and m2 are placed at the opposite ends of a rigid rod of length L, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity 0 is minimum, is given by [figure]

1. x = m2m1L
2. x = m2Lm1 + m2
3. x = m1Lm1 + m2
4. x = m1m2L