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 disc to friction is:

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