A thin circular ring of mass \( M \) and radius \( r \) is rotating about its axis with constant...

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A thin circular ring of mass \( M \) and radius \( r \) is rotating about its axis with constant angular velocity \( \omega \). Two objects, each of mass \( m \), are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by:
(A) \( \frac{(M+2 m) \omega}{2 m} \)
(B) \( \frac{2 M \omega}{M+2 m} \)
(C) \( \frac{(M+2 m)(i)}{M} \)
(D) \( \frac{M \omega}{M+2 m} \)
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