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 \(rads ^{-1}\) )

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Answer & Solution

Correct Answer

(C) \(\frac{2 M }{( M +2 m )}\)

Step-by-step Solution

Detailed explanation

Applying conservation of angular momentum

\(M R^{2} \omega=\left(M R^{2}+2 m R^{2}\right) \omega^{\prime}\)

\(\omega^{\prime}=\frac{2 M }{ M +2 m }\)

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