Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities $\omega_1$ and $\omega_2$. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is :

Question

( A ) $\frac{1}{4} I (\omega_1 - \omega_2)^2$
( B ) $\frac{1}{2} I (\omega_1 + \omega_2)^2$
( C ) $\frac{1}{8} I (\omega_1 - \omega_2)^2$
( D ) $I (\omega_1 - \omega_2)^2$