$A$ person is standing at the edge of a circular plate that is rotating with a constant angular speed about an axis passing through its center and perpendicular to its plane. If the person starts walking along the radius towards the axis, the angular velocity of the system will:

$A$ thin circular ring of mass $M$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Four objects,each of mass $m$,are kept gently on the opposite ends of two perpendicular diameters of the ring. The new angular velocity of the ring will be:

$A$ circular platform is free to rotate in a horizontal plane about a vertical axis passing through its center. $A$ tortoise is sitting at the edge of the platform. Now, the platform is given an angular velocity $\omega_0$. When the tortoise moves along a chord of the platform with a constant velocity (with respect to the platform), the angular velocity of the platform $\omega(t)$ will vary with time $t$ as:

$A$ uniform rod of length $6L$ and mass $8m$ is pivoted at its centre $C$. Two masses $m$ and $2m$ with speeds $2v$ and $v$ respectively,as shown in the figure,strike the rod and stick to it. Initially,the rod is at rest. If it rotates with angular velocity $\omega$ due to the impact,then $\omega$ will be:

Which of the following remains constant in a central force field?

If the earth suddenly shrinks to $\frac{1}{64}$th of its original volume with its mass remaining the same,the period of rotation of earth becomes $\frac{24}{x} \text{ h}$. The value of $x$ is $.......$