$A$ ring of mass $m$ and radius $r$ rotates about an axis passing through its centre and perpendicular to its plane with angular velocity $\omega$. Its kinetic energy is

$A$ ring of radius $0.5\, m$ and mass $10 \,kg$ is rotating about its diameter with an angular velocity of $20 \,rad/s.$ Its kinetic energy is .......... $J$.

$A$ 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 angular speed twice that of the sphere. The ratio of the kinetic energy of the sphere to the kinetic energy of the cylinder will be:

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

$A$ body is rotating about its own axis. Its rotational kinetic energy is $x$ and its angular momentum is $y$. Hence,its moment of inertia about its own axis is:

$A$ solid cylinder of mass $M$ and radius $R$ is rotating about its geometrical axis. $A$ solid sphere of same mass and same radius is also rotating about its diameter with an angular speed half that of the cylinder. The ratio of the kinetic energy of rotation of the sphere to that of the cylinder will be