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

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