The angular velocity of a body changes from $6 \mathrm{rad} \mathrm{s}^{-1}$ to $21 \mathrm{rad} \mathrm{s}^{-1}$ in a time of 1.5 s . If the moment of inertia of the body is $\mathrm{g} \mathrm{m}^2$, then the rate of change of angular momentum of the body is

A circular dise of diameter 0.8 m and mass 4 kg is rolling on a smooth horizontal plane. If 2.56 N m torque is acting on the disc, then its angular acceleration is

A solid sphere and a solid cylinder have same mass and same radius. The ratio of the moment of inertia of the solid sphere about its diameter and the moment of inertia of the solid cylinder about its axis is

If a solid sphere is rolling without slipping on a horizontal plane, then the ratio of its rotational and total kinetic energies is