Question

Moment of inertia of body resists a change in its state of angular momentum and depends on the mass of the body, size and shape of the body, distribution of mass about the axis of rotation, position and orientation of the axis of rotation. Three bodies, a ring, a solid sphere, a solid cylinder roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are identical.

Moment of inertia of a body about a given axis is the rotational inertia of the body about that axis. It is represented by I= MK2, where M is mass of body and K is radius of gyration of the body about that axis. It is a scalar quantity, which is measured in kgm2. When a body rotates about a given axis, and the axis of rotation also moves, then total K.E of body = K.E. of translation + K.E. of rotation E = 1/2 mv2 + 1/2 Iω2

Moment of inertia depends on

Assertion (A): Moment of inertia depends on the distribution of mass and the axis of rotation. Reason (R): Moment of inertia is a scalar quantity.