The moment of inertia of a ring about an axis passing through its centre and perpendicular to its plane is $I$. It is rotating with angular velocity $\omega$. Another identical ring is gently placed on it so that their centres coincide. If both the rings are rotating about the same axis,then the loss in kinetic energy is:

• A
  $\frac{I \omega^2}{16}$
• B
  $\frac{I \omega^2}{8}$
• C
  $\frac{I \omega^2}{4}$
• D
  $\frac{I \omega^2}{2}$