Q. A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity ω. If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity:
A) ωM/(M + 2m)
B) ω(M + 2m)/M
C) ωM/(M + m)
D) ω(M − 2m)/(M + 2m)
Explanation
[Solution from source] No external torque acts, so angular momentum is conserved: MR²ω = (MR² + 2mR²)ω′. Hence ω′ = ωM/(M + 2m). The added masses increase the moment of inertia, so the angular velocity must fall, which rules out the expression larger than ω. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.