A solid sphere and a disc of same mass $M$ and radius $R$ - are kept such that their curved surfaces are in contact and their centres lie along the same horizontal line. The moment of inertia of the two body system about an axis passing through their point of contact and perpendicular to the plane of the disc is

A thin uniform wire of mass $m$ and linear mass density $\rho$ is bent in the form of a circular loop. The moment of inertia of the loop about its diameter is

A solid sphere rolls down without slipping from the top of an inclined plane of height 28 m and angle of inclination $30^{\circ}$. The velocity of the sphere, when it reaches the bottom of the plane is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

If the radius of the earth becomes $x$ times its present value, the new period of rotation in hours is