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A small ring of mass m(1) is connected b...

A small ring of mass `m_(1)` is connected by a string of length l to a small heavy bob of mass `m_(2)`. The ring os free to move (slide) along a fixed smooth horizontal wire. The bob is given a small displacement from its equilibrium position at right angles to string. Find period of small oscillations.

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The correct Answer is:
A, B
Centre of mass will be at rest as there is no external
So effective length
`l_(eff) = ((m_(1))/(m_(1) + m_(2)))l`
`t = 2pisqrt((l_(eff))/(g)) = 2pisqrt((m_(1)l)/((m_(1) + m_(2))g))`
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