If the moment of inertia of an object is $I$ and its angular velocity is $\omega$,then its rotational kinetic energy will be:

Two bodies $A$ and $B$ have their moments of inertia $I_1$ and $I_2$ respectively about their axis of rotation. If their kinetic energies of rotation are equal and their angular momenta $L_1$ and $L_2$ respectively are in the ratio $1 : \sqrt{3}$,then $I_2$ will be

$A$ solid sphere of mass $M$ and radius $R$ is rotating about its diameter. $A$ solid cylinder of the same mass and radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation ($K_{\text{sphere}}$ to $K_{\text{cylinder}}$) will be:

If the rotational kinetic energy of a body is increased by $300\ \%$,then the percentage increase in its angular momentum will be .......... $\%$

The moments of inertia of two freely rotating bodies $A$ and $B$ are $I_{A}$ and $I_{B}$ respectively. Given $I_{A} > I_{B}$ and their angular momenta are equal. If $K_{A}$ and $K_{B}$ are their kinetic energies,then: