The moment of inertia of a body about a given axis is $2.4\ kg-m^2$.  To produce a rotational kinetic energy of $750\ J$, an angular acceleration of $5\ rad/s^2$ must be applied about that axis for.......... $\sec$

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

A fly wheel of moment of inertia $I$ is rotating at $n$ revolutions per $sec$. The work needed to double the frequency would be

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 $..........ms ^{-1}$.

$A$ uniform rod of mass $M$ is hinged at its upper end. $A$ particle of mass $m$ moving horizontally strikes the rod at its mid point elastically. If the particle comes to rest after collision find the value of $M/m =?$

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