A thin circular ring of mass 'M' and radius 'R' is rotating

Question

A thin circular ring of mass 'M' and radius 'R' is rotating about its axis with a constant angular velocity

ω

. Four objects each of mass 'm', are kept gently to the opposite ends of two perpendicular diameters of the ring. The new angular velocity of the ring will be

Options:

A . MωM+4m

B . (M+4m)ωM

C . (M−4m)ωM+4m

D . Mω4m

Answer: Option A
:
A
Initial angular momentum of ring

= I ω = M R^{2} ω

If four object each of mass m, and kept gently to the opposite ends of two perpendicular
diameters of the ring then final angular momentum

= (M R^{2} + 4 m R^{2}) ω^{'}

By the conservation of angular momentum
Initial angular momentum = Final angular momentum

M R^{2} ω = (M R^{2} + 4 m R^{2}) ω^{'} \Rightarrow ω^{'} = (\frac{M}{M + 4 m}) ω .

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