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Question

A seconds pendulum is suspended in a car that is traveling with a constant speed of $$10\ m/s$$ round a circle of radius $$10\ m$$. If the pendulum undergoes small oscillations, the time period will be


A
2 s
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B
4 s
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C
less than 2 s
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D
greater than 2 s but less than 4 s
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Solution

The correct option is D less than $$2\ s$$
The time period of a second pendulum is $$2\ s$$. When it is rotated in a circle, a centripetal acceleration also acts on pendulum towards center. So, the effective acceleration due to gravity $$g'$$ increases to $$\sqrt{g^2+a^2}$$, and we know that $$T \propto \dfrac{1}{\sqrt{g'}}$$, So the time period of the pendulum will decrease, i.e., time period will be less than 2 s

Physics

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