The ratio of rotational and translatory kinetic energies of a sphere is

$A$ solid sphere of mass $M$ and radius $R$ is rotating about its diameter. $A$ solid cylinder of the same mass and radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation ($K_{\text{sphere}}$ to $K_{\text{cylinder}}$) will be:

Rotational kinetic energy of a given body about an axis is proportional to

$A$ body having a moment of inertia about its axis of rotation equal to $3 \ kg \ m^{2}$ is rotating with an angular velocity of $3 \ rad \ s^{-1}$. The kinetic energy of this rotating body is the same as that of a body of mass $27 \ kg$ moving with velocity $v$. The value of $v$ is: (in $m \ s^{-1}$)

$A$ thin circular disc of mass $12 \,kg$ and radius $0.5 \,m$ rotates with an angular velocity of $100 \,rad/s$. The rotational kinetic energy of the disc is (in $\,kJ$)

If $L, M$,and $P$ are the angular momentum,mass,and linear momentum of a particle respectively,which of the following represents the kinetic energy of the particle when the particle rotates in a circle of radius $R$?