If the rotational kinetic energy of an object is $50\%$ of its linear kinetic energy,then the object is:

$A$ 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

$A$ thin uniform rod of length $2 \ m$,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 $\sqrt{\frac{\alpha E}{Ad}}$,then the value of $\alpha$ is $...........$

$A$ body rotating with an angular velocity of $3 \ rad/s$ has a moment of inertia of $3 \ kg \cdot m^2$ about its axis of rotation. The rotational kinetic energy of this body is equal to the translational kinetic energy of another body of mass $27 \ kg$. The speed of the $27 \ kg$ mass body is .......... $m/s$.

$A$ 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

$A$ molecule consists of two atoms each of mass $m$ and separated by a distance $d$. At room temperature,if the average rotational kinetic energy is $E$,then the angular frequency is: