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Question

The length of a simple pendulum executing simple harmonic motion is increased by 10%. The percentage increase in the time period of the pendulum due to increased length will be:

A
10%
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B
5%
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C
15%
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D
20%
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Solution

The correct option is B 5%
Let the length of simple pendulum be l.
Let the time period of oscillation of simple pendulum be T.
T=2πlg

Tl12
ΔTT=12(Δll) ...(i)
Since fractional change in length of pendulum is,
Δll=10100=0.1
substituting in Eq.(i)
ΔTT=0.05
Hence % change in time period of pendulum is.
ΔTT×100=5%
The percentage increase in the time period of the pendulum will be 5%

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