Question

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 to the opposite ends of two perpendicular diameters of the ring. The new angular velocity of the ring will be

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Initial angular momentum of ring $=I\omega =M{R}^2\omega$
If four object each of mass m, and kept gently to the opposite ends of two perpendicular
diameters of the ring then final angular momentum $=(M{R}^2+4m{R}^2){\omega }^{\prime }$
By the conservation of angular momentum
Initial angular momentum = Final angular momentum
$M{R}^2\omega =(M{R}^2+4m{R}^2){\omega }^{\prime }\Rightarrow {\omega }^{\prime }=\left(\frac{M}{M+4m}\right)\omega .$