Two discs of same moment of inertia $\left(I\right)$ are rotating in same sense 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 in energy during this process is

• A

  $\frac{1}{2}I{\left({\omega }_1+{\omega }_2\right)}^2$
• Correct answer
  B

  $\frac{1}{4}I{\left({\omega }_1-{\omega }_2\right)}^2$
• C

  $I{\left({\omega }_1-{\omega }_2\right)}^2$
• D

  $\frac{1}{8} {\left({\omega }_1-{\omega }_2\right)}^2$

Hence, the correct answer is option: 'B'.