$A$ 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:

$A$ thin circular ring of mass $M$ and radius $R$ is rotating with a constant angular velocity $2 \; rad \; s^{-1}$ in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects,each of mass $m$,are attached gently to the opposite ends of a diameter of the ring,the ring will then rotate with an angular velocity (in $rad \; s^{-1}$) of:

$A$ person of $80\, kg$ mass is standing on the rim of a circular platform of mass $200\, kg$ rotating about its axis at $5$ revolutions per minute $(rpm)$. The person now starts moving towards the centre of the platform. What will be the rotational speed (in $rpm$) of the platform when the person reaches its centre?

$A$ man standing on a turn-table is rotating at a certain angular frequency with his arms outstretched. He suddenly folds his arms. If his moment of inertia with folded arms is $75 \%$ of that with outstretched arms,then his rotational kinetic energy will

$A$ thin ring of mass $M$ and radius $R$ is rotating with an angular velocity $\omega$ about an axis passing through its center and perpendicular to its plane. If $4$ point masses each of mass $m$ are placed gently at the opposite ends of two mutually perpendicular diameters,what will be the new angular velocity of the system?

$A$ 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 $?$