The Moon revolves around the Earth in an orbit of radius $R$ with a time period of revolution $T$. It also rotates about its own axis with a time period $T$. If the mass of the Moon is $M$ and its radius is $r$,the total kinetic energy of the Moon is:

$A$ 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 $(g = \text{acceleration due to gravity})$

$A$ disc of mass $1\,kg$ and radius $R$ is free to rotate about a horizontal axis passing through its centre and perpendicular to the plane of the disc. $A$ body of the same mass as that of the disc is fixed at the highest point of the disc. Now the system is released. When the body comes to the lowest position,its angular speed will be $4 \sqrt{\frac{x}{3 R}} \text{ rad s}^{-1}$ where $x=$ (Given $g = 10 \text{ m s}^{-2}$)

$A$ 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

$A$ thin meter rod is placed with one end on the ground. It is allowed to fall such that the contact point remains fixed. Find the velocity of the upper end when it hits the ground.

$A$ 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):