$A$ constant power is supplied to a rotating disc. The angular velocity $(\omega)$ of the disc varies with the number of rotations $(n)$ made by the disc as:

$A$ thin,uniform metal rod of mass $M$ and length $L$ is swinging about a horizontal axis passing through its end. Its maximum angular velocity is $\omega$. Its centre of mass rises to a maximum height of $(g = \text{acceleration due to gravity})$

$A$ thin uniform rod of length $L$ and mass $M$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of (where $g$ is the acceleration due to gravity):

$A$ thin uniform rod $AB$ of mass $m$ and length $l$ is hinged at one end $A$ to the ground level. Initially, the rod stands vertically and is allowed to fall freely to the ground in the vertical plane. The angular velocity of the rod when its $B$ end strikes the ground is $(g = \text{acceleration due to gravity})$

$A$ uniform solid cylinder of mass $M$ and radius $R$ can freely rotate around its axis $O$. There is an elastic string of relaxed length $L$ and stiffness $K$ attached to the cylinder and a static wall. Initially,the string is relaxed. As the cylinder starts rotating,the string will wind around the cylinder. The surface of the cylinder is very rough,so the string does not slip on the cylinder's surface. The minimum initial angular speed of the cylinder,${\omega _0}$,so that it can rotate through an angle $2\pi$ is (Assume Hooke's law to be valid.)

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