If the radius of the earth is reduced to three-fourth of its present value without any change in its mass,then the duration of the day on earth will be . . . . . . hours $30$ minutes.

Before diving into a swimming pool, a swimmer curls their body, because this

Two discs of same moment of inertia $I$ are rotating about their central axes perpendicular to their planes with angular velocities $\omega_1$ and $\omega_2$. They are brought into contact face to face,such that their axes of rotation coincide. The expression for the loss of energy during this process is:

$A$ disc of moment of inertia $I_1$ is rotating in a horizontal plane about an axis passing through its center and perpendicular to its plane with a constant angular speed $\omega_1$. Another disc of moment of inertia $I_2$ having zero angular speed is placed coaxially on the rotating disc. Now,both the discs are rotating with a constant angular speed $\omega_2$. The energy lost by the initial rotating disc is

$A$ thin circular disc of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity $\omega$. If another disc of same dimensions but of mass $M/2$ is placed gently on the first disc co-axially,then the new angular velocity of the system is:

$A$ disc of mass $M$ and radius $R$ is rolling with angular speed $\omega$ on a horizontal plane as shown. The magnitude of angular momentum of the disc about the origin $O$ is