A solid sphere of mass $2\,kg$ is making pure rolling on a horizontal surface with kinetic energy $2240\,J$. The velocity of centre of mass of the sphere will be $..........ms ^{-1}$.

If a body completes one revolution in $\pi $ $sec$ then the moment of inertia would be

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

A disc of radius $1\,m$ and mass $4\,kg$ rolls on a horizontal plane without slipping in such a way that its centre of mass moves with a speed of $10\,cm/\sec .$ Its rotational kinetic energy is

The angular momentum of a rigid body of mass m about an axis is $n$ times the linear momentum $(P)$ of the body. Total kinetic energy of the rigid body is

A circular disc of mass $M$ and radius $R$ is rotating about its axis with angular speed $\omega_{1}$ If another stationary disc having radius $\frac{ R }{2}$ and same mass $M$ is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed $\omega_{2}$. The energy lost in the process is $p \%$ of the initial energy. Value of $p$ is