The Sun rotates around its centre once in $27$ days. What will be the period of revolution if the Sun were to expand to twice its present radius without any external influence (in $days$)? Assume the Sun to be a sphere of uniform density.

$A$ thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Two objects,each of mass $m$,are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity:

The angular momentum of a system of particles is not conserved:

$A$ force $\overrightarrow{F} = \alpha \hat{i} + 3\hat{j} + 6\hat{k}$ is acting at a point $\overrightarrow{R} = 2\hat{i} - 6\hat{j} - 12\hat{k}$. The value of $\alpha$ for which angular momentum about the origin is conserved is

An ant is sitting on the edge of a rotating disc. If the ant walks along the diameter to reach the other end, how will the angular velocity of the disc change?

Two wheels $A$ and $B$ are mounted on the same axis. The moment of inertia of wheel $A$ is $I_A$ and its angular velocity is $\omega_A$,while wheel $B$ is initially at rest. When they are coupled together by a clutch,they rotate with a common angular velocity $\omega$. What is the moment of inertia of wheel $B$?