Two bodies have their moments of inertia $I$ and $2I$ respectively about their axis of rotation. If their kinetic energies of rotation are equal,their angular momentum will be in the ratio

$A$ 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

$A$ 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:

$A$ rigid body rotates with an angular momentum $L$. If its rotational kinetic energy is made four times, its angular momentum will become

$A$ 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 .......... $J$.

Two objects have moments of inertia $I_1$ and $I_2$ $(I_1 > I_2)$ and their angular velocities are equal. If their rotational kinetic energies are $E_1$ and $E_2$ respectively,then: