Question

A thin circular ring of mass $M$ and radius $R$ is rotating with a constant angular velocity $2\, rads ^{-1}$ 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 $m$ be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in $rads ^{-1}$ ).

• A. $\frac{M}{(M+m)}$
• B. $\frac{( M +2 m )}{2 M }$
• C. $\frac{2 M}{(M+2 m)}$
• D. $\frac{2( M +2 m )}{ M }$

Answer 1

Answer: (C)

Applying conservation of angular momentum
$MR ^{2} \omega=\left( MR ^{2}+2 mR ^{2}\right) \omega^{\prime}$
$\omega^{\prime}=\frac{2 M}{M+2 m}$