$A$ 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 spherical ball of mass $1 \, kg$ and radius $3 \, cm$ is rotating with an angular velocity of $50 \, rad/s$ about an axis passing through its center. The rotational kinetic energy is:

$A$ 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:

$A$ solid cylinder of mass $M$ and radius $R$ is rotating about its geometrical axis. $A$ solid sphere of the 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

$A$ uniform thin rod of length $l$ and mass $m$ is suspended from one of its ends and is rotated at $f$ rotations per second. The rotational kinetic energy of the rod will be

$A$ particle of mass '$m$' is performing uniform circular motion along a circular path of radius '$r$'. Its angular momentum about the axis passing through the centre and perpendicular to the plane is '$L$'. The kinetic energy of the particle is