The angular velocity of a body is $\mathop \omega \limits^ \to   = 2\hat i + 3\hat j + 4\hat k$ and a torque $\mathop \tau \limits^ \to   = \hat i + 2\hat j + 3\hat k$ acts on it. The rotational power will be .......... $W$

The ratio of rotational and translatory kinetic energies of a sphere is                

A ball rolls without slipping.  The radius of gyration of the ball about an axis passing through its centre of mass $K$. If radius of the ball be $R$, then the fraction of total energy associated with its rotational energy will be 

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

Explain work done by torque.

Point masses $m_1$ and $m_2$ 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 $\omega_0$ is minimum, is given by