Two bodies $A$ and $B$ have their moments of inertia $I_1$ and $I_2$ respectively about their axis of rotation. If their kinetic energies of rotation are equal and their angular momenta $L_1$ and $L_2$ respectively are in the ratio $1 : \sqrt{3}$,then $I_2$ will be

Two identical particles each of mass $m$ are separated by a distance $d$. The axis of rotation passes through the midpoint of $d$ and is perpendicular to the length $d$. If $K$ is the rotational kinetic energy of the system,then the angular frequency $\omega$ is:

$A$ solid cylinder of mass $20 \; kg$ rotates about its axis with angular speed $100 \; rad \; s^{-1}$. The radius of the cylinder is $0.25 \; m$. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

$A$ 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:

$A$ rigid body rotates with an angular momentum $L$. If its rotational kinetic energy is made four times, its angular momentum will become

$A$ 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