A body is rotating about its own axis. Its rotational kinetic energy is '$x$' and its angular momentum is '$y$'. Hence its moment of inertia about its own axis is

A force of $3\hat{i} + 2\hat{j} - \hat{k}$ N acts on a particle with position vector $\hat{i} + \hat{j} - \hat{k}$ m. The magnitude of torque of given force is

A thin uniform rod AB of mass '$m$' and length '$l$' is hinged at one end A to the ground level. Initially the rod stands vertically and is allowed to fall freely to the ground in the vertical plane. The angular velocity of the rod when its B end strikes the ground is
($g$ = acceleration due to gravity)

The radius of gyration of a solid sphere of radius 'R' and mass 'M' about its diameter is $K_d$ and that about a tangent of a solid sphere is $K_t$. The ratio of $K_d$ to $K_t$ is