If the earth were to suddenly contract to $\frac{1}{n}^{th}$ of its present radius without any change in its mass,the duration of the new day will be nearly:

$A$ uniform disc of mass $m_0$ rotates freely about a fixed horizontal axis passing through its centre. $A$ thin cotton pad is fixed to its rim,which can absorb water. The mass of water dripping onto the pad per unit time is $\mu$. After what time will the angular velocity of the disc get reduced to half its initial value?

$A$ disc of mass $M$ and radius $R$ is moving with an angular velocity $\omega$ as shown in the figure. Find the angular momentum of the disc about the reference point $O$.

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.

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:

$A$ thin circular ring of mass $m$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Two objects each of mass $M$ are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity $\omega '$ equal to: