$A$ flywheel rotating about a fixed axis has a kinetic energy of $360 \ J$ when its angular speed is $30 \ rad/s$. The moment of inertia of the wheel about the axis of rotation is ...... $kg \ m^2$.

$A$ solid sphere of mass $M$ and radius $R$ is rotating about its diameter. $A$ disc of the same mass and radius is also rotating about an axis passing through its centre and perpendicular to the plane,but its angular speed is twice that of the sphere. The ratio of the kinetic energy of the disc to that of the sphere is: (in $: 1$)

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?

$A$ solid sphere of mass $m$ and radius $R$ is rotating about its diameter. $A$ solid cylinder of the same mass and same 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 $E_{sphere}/E_{cylinder}$ will be

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:

Three identical square plates rotate about the axes shown in the figure in such a way that their kinetic energies are equal. Each of the rotation axes passes through the centre of the square. Then the ratio of angular speeds $\omega_{1}: \omega_{2}: \omega_{3}$ is