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 contacl face to face coinciding the axis of rotation. The expression for loss of energy during this process is

Question

$\begin{array}{1 1} (1) \frac{1}{2} I (\omega_1+\omega_2)^2 \\ (2) \frac{1}{4} I (\omega_1-\omega_2)^2 \\ (3) I (\omega_1+\omega_2)^2 \\ (4) \frac{1}{8} (\omega_1-\omega_2)^2 \end{array}$