A circular disk of moment of inertia it 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 disc to friction is –

Question

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