$A$ circular disc of mass $20 \ kg$ and radius $1 \ m$ is rotating about an axis passing through its center and perpendicular to its plane with an angular velocity of $2 \ rad \ s^{-1}$. Then the rotational kinetic energy of the disc is (in $J$)

$A$ body completes one rotation in $1 \ s$. What is its moment of inertia if its rotational kinetic energy is $E_R$?

Two bodies $A$ and $B$ are rotating freely with moments of inertia $I_A$ and $I_B$ respectively. Given $I_A > I_B$ and their angular momenta are equal. If $K_A$ and $K_B$ are their rotational kinetic energies,then:

$A$ solid sphere of mass $m$ and radius $R$ is rotating about its diameter. $A$ solid cylinder of the same mass and same 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 $E_{sphere}/E_{cylinder}$ will be

If the rotational kinetic energy is $50\%$ of the total kinetic energy,then the body is a .......... .

Three particles are situated on a light and rigid rod along the $Y$-axis as shown in the figure. If the system is rotating with an angular velocity of $2 \, rad/s$ about the $X$-axis,then the total kinetic energy of the system is ...... $J$.