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

$A$ 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:

$A$ thin uniform rod of length $L = 2 \text{ m}$, cross-sectional area $A$, and density $d$ is rotated about an axis passing through its center and perpendicular to its length with angular velocity $\omega$. If the value of $\omega$ in terms of its rotational kinetic energy $E$ is $(\alpha E/Ad)^{1/2}$, then the value of $\alpha$ is:

$A$ 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 ratio of rotational and translatory kinetic energies of a sphere is

$A$ 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