A circular disc of moment of inertia ${\mathrm{I}}_{\mathrm{i}}$ is rotating in a horizontal plane, about its geometrical axis, with a constant angular speed ${\mathrm{\omega }}_{\mathrm{i}}$. Another disc of moment of inertia ${\mathrm{I}}_f$ 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 ${\mathrm{\omega }}_{\mathrm{f}}$. The energy lost by the initially rotating disc due to friction is:

• A

  $\frac{1}{2}\frac{{{\mathrm{I}}_f}^2}{({\mathrm{I}}_{\mathrm{i}}+{\mathrm{I}}_f)}{{\mathrm{\omega }}_{\mathrm{i}}}^2$

• B

  $\frac{1}{2}\frac{{{\mathrm{I}}_{\mathrm{i}}}^2}{({\mathrm{I}}_{\mathrm{t}}+{\mathrm{I}}_f)}{{\mathrm{\omega }}_{\mathrm{i}}}^2$

• C

  $\frac{1}{2}\frac{{\mathrm{I}}_{\mathrm{f}}-{\mathrm{I}}_i}{({\mathrm{I}}_f+{\mathrm{I}}_i)}{{\mathrm{\omega }}_{\mathrm{i}}}^2$

• D

  $\frac{1}{2}\frac{{\mathrm{I}}_i{\mathrm{I}}_f}{({\mathrm{I}}_i+{\mathrm{I}}_f)}{{\mathrm{\omega }}_{\mathrm{i}}}^2$