$A$ 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 $\omega '$ equal to:

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