If the radius of the Earth becomes $1/n^{th}$ of its present value,without any change in its mass,then the duration of the day becomes:

$A$ solid sphere is rotating in space. If the radius of the sphere is increased while keeping its mass constant,which of the following physical quantities will not change?

In the absence of torque,the rotational frequency of a body changes from $1 \text{ cy/sec}$ to $16 \text{ cy/sec}$. The ratio of the radius of gyration in the two cases will be: (in $: 1$)

Assertion $:-$ When no external torque is applied and moment of inertia of a rotating body changes,then its angular momentum remains conserved,but its kinetic energy changes.
Reason $:-$ Angular momentum does not depend upon moment of inertia of the body.

$A$ circular disc is rotating with an angular velocity $\omega$. If a child sits on the disc,which of the following quantities will be conserved?

The angular momentum of a moving body remains constant if