A uniform solid cylinder with radius R and length L has moment of inertia $I_1$ about the axis of the cylinder. A concentric solid cylinder of radius $R/2$ and length $L/2$ is carved out of the original cylinder. If $I_2$ is the moment of inertia of the carved out portion of the cylinder then $I_1/I_2$ is (Both $I_1$ and $I_2$ are about the axis of the cylinder)

Solid sphere is rotating about an axis as shown in figure. If the radius of the sphere is 5 cm, then radius of gyration about that axis will be $\sqrt{x}$ cm. The value of x is

A Solid sphere has mass M and radius R. Its moment of inertia about a parallel axis passing through a point at a distance R/3 from its centre is

The power (P) is supplied to rotating body having moment of inertia 'I' and angular acceleration '$\alpha$'. Its instantaneous angular velocity is