System of Particles and Rotational Motion

The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is

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

A particle of mass m moves in the XY plane with a velocity v along the straight line AB. If the angular momentum of the particle with respect to origin O is LA when it is at A and LB when it is at B, then [figure]

1. LA = LB
2. the relationship between LA and LB depends upon the slope of the line AB
3. LA < LB
4. LA > LB

A uniform rod AB of length l and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is ml23, the initial angular acceleration of the rod will be [figure]

1. mgl2
2. 32gl
3. 3g2l
4. 2g3l

A wheel has angular acceleration of 3.0 rad/sec2 and an initial angular speed of 2.00 rad/sec. In a time of 2 sec it has rotated through an angle (in radian) of

1. 10
2. 12
3. 4
4. 6

A uniform rod AB of length l and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is ml23, the initial angular acceleration of the rod will be

1. mgl2
2. 32gl
3. 3g2l
4. 2g3l

The moment of inertia of a uniform circular disc of radius R and mass M about an axis touching the disc at its diameter and normal to the disc

1. 12MR2
2. MR2
3. 25MR2
4. 32MR2

The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing through the edge of the disc and normal to the disc is

1. MR2
2. 12MR2
3. 32MR2
4. 72MR2

A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle . The frictional force

1. dissipates energy as heat
2. decreases the rotational motion
3. decreases the rotational and translational motion
4. converts translational energy to rotational energy.

Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular velocity will be in the ratio

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

Three particles, each of mass m gram, are situated at the vertices of an equilateral triangle ABC of side l cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram-cm2 units will be [figure]

1. 34ml2
2. 2ml2
3. 54ml2
4. 32ml2