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:

1. A
   $\frac{1}{2}I({\omega }_1+{\omega }_2{)}^2$
2. B
   $\frac{1}{4}I({\omega }_1-{\omega }_2{)}^2$
3. C
   $I({\omega }_1-{\omega }_2{)}^2$
4. D
   $\frac{1}{8}I({\omega }_1-{\omega }_2{)}^2$