Three objects,$A$ (a solid sphere),$B$ (a thin circular disk),and $C$ (a circular ring),each have the same mass $M$ and radius $R$. They all spin with the same angular speed $\omega$ about their own symmetry axes. The amounts of work $(W)$ required to bring them to rest would satisfy the relation:

$A$ rod of length $l$ is hinged at one end. It is brought to a horizontal position and released. The angular velocity of the rod when it is in the vertical position is

$A$ man, sitting firmly on a rotating stool, has his arms stretched. If he folds his arms, the work done by the man is:

To maintain a rotor at a uniform angular speed of $200 \; rad \; s^{-1}$,an engine needs to transmit a torque of $180 \; N \; m$. What is the power required by the engine (in $; kW$)? (Note: uniform angular velocity in the absence of friction implies zero torque. In practice,applied torque is needed to counter frictional torque). Assume that the engine is $100 \%$ efficient.

$A$ uniform rod of length $2L$ is placed with one end in contact with a horizontal surface. The other end is released from an angle $\alpha$ with the horizontal,such that the end in contact does not slip. What will be its angular velocity when it becomes horizontal?

$A$ thin uniform circular disc of mass $\frac{10}{\pi^2} \,kg$ and radius $2 \,m$ is rotating about an axis passing through its centre and perpendicular to its plane. The work done to increase the angular speed of the disc from $90 \,rev/min$ to $120 \,rev/min$ is (in $\,J$)