JEE Main202226 Jun 2022Morning ShiftPhysicsRotational MotionActual
A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rad s - 1 in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass m be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in rad s - 1 ).
Options
- AM M + m
- BM + 2 m 2 M
- C2 M M + 2 m
- D2 M + 2 m M
Correct answer
C. 2 M M + 2 m
Step-by-step solution
As the masses are gently placed we can apply conservation of angular momentum. Initial moment of Inertia I 1 = M R 2 Final moment of inertia I 2 = M R 2 + 2 m R 2 By conservation of angular momentum I 1 ω 1 = I 2 ω 2 ⇒ M R 2 × 2 = M + 2 m R 2 × ω 2 ⇒ ω 2 = 2 M M + 2 m   rad   s - 1