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

If the angular momentum of a rotating body is increased by $200\ \%$,then its kinetic energy of rotation will be increased by .......... $\%$

$A$ spherical solid ball of $10\,kg$ mass and radius $3\,cm$ is rotating about an axis passing through its centre with an angular velocity of $50\,rad/s$. The kinetic energy of rotation is ....... $J$.

The moments of inertia of two bodies about their axes of rotation are $I$ and $2I$ respectively. If their rotational kinetic energies are equal,what is the ratio of their angular velocities?

$A$ rod of length $L$ revolves in a horizontal plane about an axis passing through its centre and perpendicular to its length. The angular velocity of the rod is $\omega$. If $A$ is the area of cross-section of the rod and $\rho$ is its density, then the rotational kinetic energy of the rod is

$A$ solid cylinder of mass $20 \; kg$ rotates about its axis with angular speed $100 \; rad \; s^{-1}$. The radius of the cylinder is $0.25 \; m$. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?