A pendulum has time period T for small oscillations. An obstacle P is situated below the point of suspension O at a distance 3 l 4 . The pendulum is released from rest. Throughout the motion the movin

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A pendulum has time period T for small oscillations. An obstacle P is situated below the point of suspension O at a distance 3 l 4 . The pendulum is released from rest. Throughout the motion the moving string makes small angles with vertical. Time after which the pendulum returns back to its initial position is -

TestHub · Accepted Answer

first half oscillation is covered with length $l$ and second half with length $\frac{3 l}{4}$ therefore total time can be measured by

$t = \frac{T_{1}}{2} + {\frac{T_{2}}{2}}_{}$

$T_{1} = 2 π \sqrt{\frac{1}{g}} = T$

$T_{2} = 2 π \sqrt{\frac{1 / 4}{g}} = \frac{T}{2}$

Putting value we get $t = \frac{3 T}{4}$

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