A rod of length $L$ revolves in a horizontal plane about the axis passing through its centre and perpendicular to its length. The angular velocity of the rod is $\omega$. If $A$ is the area of cross-section of the rod and $\rho$ is its density, then the rotational kinetic energy of the rod is

A solid sphere and a solid cylinder, each of mass $M$ and radius $R$ are rolling with a linear speed on a flat surface without slipping. Let $L_1$ be magnitude of the angular momentum of the sphere with respect to a fixed point along the path of the sphere. Likewise $L_2$ be the magnitude of angular momentum of the cylinder with respect to the same fixed point along its path. The ratio $L_1 / L_2$ is

An object of mass 2 kg is hanging from a rope that is wrapped around a pulley of radius 25 cm . The mass of pulley is 2 kg . Find the acceleration of the object. (Assume, pulley to be a solid disk $g=10 \mathrm{~m} / \mathrm{s}^2$ )