JEE Main · 2022 · 26 Jun 2022 · Shift 1 · Rotational Mechanics

A thin circular ring of mass

M

and radius

R

is rotating with a constant angular velocity

2 rads^{- 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 rads

^{- 1}

Answer: (C)

Solution

By conservation of angular momentum (no external torque),

L_{i} = L_{f}

. Initial angular momentum:

L_{i} = I_{i} ω_{i} = M R^{2} \times 2

. Final angular momentum:

L_{f} = I_{f} ω^{'} = (M R^{2} + 2 m R^{2}) ω^{'}

. Equating:

2 M R^{2} = (M + 2 m) R^{2} ω^{'}

, giving

ω^{'} = \frac{2 M}{M + 2 m}

rad/s.

JEE Main · 2022 · 26 Jun 2022 · Shift 1 · Single correct option