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

A

$$I (\omega_1 - \omega_2)^2$$

B

$$\frac{I}{8}(\omega_1 - \omega_2)^2$$

C

$$\frac{1}{2}I(\omega_1 + \omega_2)^2$$

D

$$\frac{1}{4}I(\omega_1 - \omega_2)^2$$