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

$A$ 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 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:

$A$ wheel (rim) of mass $6 \ kg$ and radius $40 \ cm$ is rotating at a rate of $300 \ rpm$. The rotational kinetic energy of the wheel is:

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 $R$?

$A$ flywheel is in the form of a solid circular disc with a mass of $72 \ kg$ and a radius of $0.5 \ m$. If it rotates at $70 \ rpm$,its rotational kinetic energy is ........ $J$.