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Question

A simple pendulum is suspended from the ceiling of a car accelerating uniformly on a horizontal road. If the acceleration is a0 and the length of the pendulum is l, find the time period of small oscillations about the mean position
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A
πl(a20+g2)1/2
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B
2πl(a20+2g2)1/2
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C
2πl(a20+g2)1/4
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D
πl(a20+g2)1/4
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Solution

The correct option is C 2πl(a20+g2)1/4
Time period of simple pendulum T=2πlgeff
In the car frame, the pendulum experiences a pseudo force in the backward direction.
Thus effective acceleration due to gravity geff=a2o+g2
T=2πla2o+g2=2πl(a2o+g2)1/4

705081_571926_ans_7f3da658c4ba4659805442ba4d3e14c2.png

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