The moment of inertia of a body about a given axis,rotating with an angular velocity of $1 \ rad/s$,is numerically equal to '$P$' times its rotational kinetic energy. The value of '$P$' is:

If the angular momentum of a body is increased by $200\%$,then the percentage increase in its rotational kinetic energy will be ........ $\%$.

$A$ 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:

Write the formula for rotational kinetic energy.

$A$ 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

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