A solid sphere of mass M and a disc of mass $\dfrac{M}{2}$ have the same radius. The ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be

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 body of mass m is taken from earth surface to a height h equal to twice the radius of earth, the increase in potential energy will be ($g$ = acceleration due to gravity on earth's surface) (R - radius of earth)