Two discs of same moment of inertia rotating about their  respective geometrical axis passing through centre and perpendicular to the plane of disc with angular velocities ${\mathrm{\omega }}_1 \mathrm{and} {\mathrm{\omega }}_2$. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is

• A

  $\frac{1}{4}\mathrm{I}{({\mathrm{\omega }}_1-{\mathrm{\omega }}_2)}^2$

• B

  $\mathrm{I}{({\mathrm{\omega }}_1-{\mathrm{\omega }}_2)}^2$

• C

  $\frac{1}{8}\mathrm{I}{({\mathrm{\omega }}_1-{\mathrm{\omega }}_2)}^2$

• D

  $\frac{1}{2}\mathrm{I}{({\mathrm{\omega }}_1+{\mathrm{\omega }}_2)}^2$