Q. 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 :
A) $\frac{1}{2}I(\omega_1 + \omega_2)^2$
B) $\frac{1}{4}I(\omega_1 - \omega_2)^2$
C) $I(\omega_1 - \omega_2)^2$
D) $\frac{I}{8}(\omega_1 - \omega_2)^2$
Explanation
[Solution] Common $\omega = (\omega_1 + \omega_2)/2$; energy loss $= \frac{1}{2}I(\omega_1^2 + \omega_2^2) - I\omega^2 = \frac{I}{4}(\omega_1 - \omega_2)^2$. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.