Two bodies $A$ and $B$ have moments of inertia $I_A$ and $I_B$, and angular momenta $L_A$ and $L_B$ respectively. Both of them have the same kinetic energy of rotation. The ratio of $L_A$ to $L_B$ is:

If a body completes one revolution in $\pi \ s$,then the moment of inertia is related to the rotational kinetic energy $(K)$ by which of the following expressions?

$A$ kathak dancer is standing on a horizontal surface with folded hands. Initially, the dancer is rotating about his central axis, and his kinetic energy is $K$. The dancer then stretches his arms such that the moment of inertia becomes three times its initial value and the angular velocity becomes one-third of its initial value. The kinetic energy of the dancer now is:

Two bodies have their moments of inertia $I$ and $2I$ respectively about their axis of rotation. If their kinetic energies of rotation are equal,their angular momentum will be in the ratio

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

Two metallic spheres of equal outer radii are found to have the same moment of inertia about their respective diameters. Which of the following statement$(s)$ is/are true?