A thin circular ring of mass $m$ and radius $R$ is rotating about its axis with a 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 an angular velocity $\omega' =$\\
(1) $\frac{\omega m}{(m + 2M)}$\\
(2) $\frac{\omega(m + 2M)}{m}$\\
(3) $\frac{\omega(m - 2M)}{(m + 2M)}$\\
(4) $\frac{\omega m}{(m + M)}$