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A pendulum has a period T for small osci...

A pendulum has a period `T` for small oscillations. An obstacle is placed directly beneath the pivot, so that only the lowest one - quarter of the string can follow the pendulum bob when it swings to the left of its resting position. The pendulum is released from rest at a certain point. How long will it take to return to that point again ? In answering this question, you may assume that the angle between the moving string and the vertical stays small throughout the motion.

Text Solution

Verified by Experts

The correct Answer is:
B
Half the oscillation is completed with length `l` and rest half with length `(l)/(4)`.
`T = (T_(1))/(2) + (T_(2))/(2) = (1)/(2)[2pisqrt((l)/(g)) + 2pisqrt((l)/((4)/(g)))]`
`= (3)/(4)[2pi sqrt((l)/(g))] = (3)/(4) T`, where `T = 2pi sqrt((l)/(g)`
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