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Question

The length of a simple pendulum is made one-ninth. Its time period becomes____its initial value.


A

nine times

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B

half

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C

one-third

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D

twice

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Solution

The correct option is C

one-third


We have time period of a pendulum Tl

T1T2=l1l2 where T1 and T2 are the initial and final time periods of the simple pendulum and l1 and l2 are the initial and final lengths of the pendulum. If the length of the simple pendulum is made one-ninth i.e.,l2=l19

T1T2=l1l19 T1T2=9 T1T2=3 T2=13 T1

i.e., the time period of the pendulum becomes one third its initial value.


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