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

$A$ uniform circular disc of mass $50 \ kg$ and radius $0.4 \ m$ is rotating with an angular velocity of $10 \ rad \ s^{-1}$ about its own axis,which is vertical. Two uniform circular rings,each of mass $6.25 \ kg$ and radius $0.2 \ m$,are gently placed symmetrically on the disc in such a manner that they are touching each other along the axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest relative to the disc and the system rotates about the original axis. The new angular velocity (in $rad \ s^{-1}$) of the system is:

$A$ solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere $?$

$A$ 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 $O$.

$A$ train is moving slowly at $2 \, m/s$ next to a railway platform. $A$ man,$1.5 \, m$ tall,alights from the train such that his feet are fixed on the ground. Taking him to be a rigid body,the instantaneous angular velocity (in $rad/s$) is

$A$ 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: