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

• 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
  $\frac{I_b - I_t}{(I_t + I_b)} \omega_i^2$