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 B5% Let the length of simple pendulum be ′l′.
Let the time period of oscillation of simple pendulum be ′T′. T=2π√lg
∵T∝l12 ⇒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%