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Question

# A simple pendulum is taken to a place where the acceleration due to gravity falls to one-fourth. The time period of the pendulum becomes ___ its initial value.

A

twice

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B

four times

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C

eight times

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D

half

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Solution

## The correct option is A twice We have time period of a pendulum T∝1√g. ∴T1T2=√g2g1 where T1 and T2 are the initial and final time periods of the simple pendulum and g1 and g2 are the initial and final time acceleration due to gravity. If the acceleration due to gravity falls to one-fourth i.e.,g2=g14 ⇒T1T2=√g14 g1 ⇒T1T2=12 ⇒T2=2 T1 i.e., the time period of the pendulum becomes twice its initial value.

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