$A$ disc of moment of inertia $I_1$ is rotating in a horizontal plane about an axis passing through its center and perpendicular to its plane with a constant angular speed $\omega_1$. Another disc of moment of inertia $I_2$ having zero angular speed is placed coaxially on the rotating disc. Now,both the discs are rotating with a constant angular speed $\omega_2$. The energy lost by the initial rotating disc is

• A
  $\frac{1}{2}\left[\frac{I_1+I_2}{I_1 I_2}\right] \omega_1^2$
• B
  $\frac{1}{2}\left[\frac{I_1 I_2}{I_1-I_2}\right] \omega_1^2$
• C
  $\frac{1}{2}\left[\frac{I_1-I_2}{I_1 I_2}\right] \omega_1^2$
• D
  $\frac{1}{2}\left[\frac{I_1 I_2}{I_1+I_2}\right] \omega_1^2$