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Q.

A thin circular ring of mass M and radius R is rotating in a horizontal plane about on axis vertical to its plane with a constant angular velocity W. 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

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a

$\frac{W (M - 2 m)}{M + 2 m}$

b

$\frac{WM}{M + 2 m}$

c

$\frac{WM}{M + m}$

d

$\frac{W (M + 2 m)}{M}$

answer is A.

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Detailed Solution

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Here the angular momentum is conserved

$I_{1} W_{1} = I_{2} W_{2} W_{2} = \frac{I_{1} W_{1}}{I_{2}} = \frac{{Mr}^{2} W}{(M + 2 m) r^{2}}$

$\Rightarrow W_{2} = \frac{MW}{M + 2 m}$

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A thin circular ring of mass M and radius R is rotating in a horizontal plane about on axis vertical to its plane with a constant angular velocity W. 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