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A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity $ω$ . Two objects each of mass m are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity

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$ω (M - 2 m) / (M + 2 m)$

$ω M / (M + 2 m)$

$ω (M + 2 m) / M$

$ω M / (M + m)$

answer is B.

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Detailed Solution

By the principle of conservation of angular momentum ,

$\begin{array}{l} Ι_{1} ω_{1} = Ι_{2} ω_{2} \\ M R^{2} ω = (M + 2 m) R^{2} ω^{'} \\ ω^{'} = \frac{M ω}{(M + 2 m)} \end{array}$

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