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 $L, M$,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 $R$?

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:

The angular momentum of a body rotating about a fixed axis is increased by $10\%$. What is the percentage increase in its rotational kinetic energy (in $\%$)?

$A$ body is rotating about its own axis. Its rotational kinetic energy is $x$ and its angular momentum is $y$. Hence,its moment of inertia about its own axis 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: