$A$ circular disc of moment of inertia $I_t$ is rotating in a horizontal plane about its symmetry axis with a constant angular speed $\omega_i$. Another disc of moment of inertia $I_b$ is dropped coaxially onto the rotating disc. Initially,the second disc has zero angular speed. Eventually,both the discs rotate with a constant angular speed $\omega_f$. The energy lost by the initially rotating disc to friction is:

• A
  $\frac{1}{2} \frac{I_b^2}{(I_t + I_b)} \omega_i^2$
• B
  $\frac{1}{2} \frac{I_t^2}{(I_t + I_b)} \omega_i^2$
• C
  $\frac{1}{2} \frac{(I_b - I_t)}{(I_t + I_b)} \omega_i^2$
• D
  $\frac{1}{2} \frac{I_b I_t}{(I_t + I_b)} \omega_i^2$