Two discs of same moment of inertia $I$ are rotating about their central axes perpendicular to their planes with angular velocities $\omega_1$ and $\omega_2$. They are brought into contact face to face,such that their axes of rotation coincide. The expression for the loss of energy during this process is:

• A
  $I{\left( {{\omega _1} - {\omega _2}} \right)^2}$
• B
  $\frac{I}{8}{\left( {{\omega _1} - {\omega _2}} \right)^2}$
• C
  $\frac{I}{2}{\left( {{\omega _1} + {\omega _2}} \right)^2}$
• D
  $\frac{I}{4}{\left( {{\omega _1} - {\omega _2}} \right)^2}$