$A$ thin circular ring of mass $M$ and radius $R$ is rotating about a transverse axis passing through its centre with constant angular velocity $\omega$. Two objects each of mass $m$ are attached gently to the opposite ends of a diameter of the ring. What is the new angular velocity?

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