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Q.

A small bead of mass m moving with velocity v gets threaded on a stationary semicircular ring of mass m and radius R kept on a horizontal table. The ring can freely rotate about its center The bead comes to rest relative to the ring. What will be the final angular velocity of the system?

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a

$\frac{2 v}{R}$

b

$\frac{3 v}{R}$

c

$\frac{v}{2 R}$

d

$\frac{v}{R}$

answer is C.

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Detailed Solution

detailed_solution_thumbnail

Using conversation of angular momentum about O, we get

$L_{i} = L_{f} \Rightarrow m v R = (m R^{2} + m R^{2}) ω \Rightarrow ω = \frac{v}{2 R}$

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A small bead of mass m moving with velocity v gets threaded on a stationary semicircular ring of mass m and radius R kept on a horizontal table. The ring can freely rotate about its center The bead comes to rest relative to the ring. What will be the final angular velocity of the system?