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

$A$ particle is moving in a uniform circular motion. At which point in the plane of the circle will the angular momentum of the particle be conserved?

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:

$A$ 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 will now rotate with an angular velocity:

$A$ uniform rod $AB$ of length $L$ and mass $M$ is pivoted at its center $O$ such that it can rotate freely in a vertical plane. The rod is initially in a horizontal position. $A$ particle $S$ of the same mass $M$ falls vertically with velocity $v$ and strikes the rod at point $C$. $C$ is the midpoint between $O$ and $B$. Find the angular velocity of the rod immediately after the particle strikes it.

$A$ man is standing on the edge of a circular platform. The platform is rotating with a constant angular velocity about an axis passing through its center and perpendicular to its plane. If the man walks along the radius towards the axis, the angular velocity will ........ .