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CGP EDU Academic Team
Published on: September 12, 2026
A simple pendulum is executing simple harmonic motion with a time period T. If the length of the pendulum is increased by 21%, the percentage increase in the time period of the pendulum of increased length is
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Verified by ExpertsThe correct answer is:
A
If initial length $l_1 = 100$ then $l_2 = 121$
By using $T = 2 \pi \sqrt{\frac{l}{g}} \Rightarrow \frac{T_1}{T_2} = \sqrt{\frac{l_1}{l_2}}$
Hence, $\frac{T_1}{T_2} = \sqrt{\frac{100}{121}} \Rightarrow T_2 = 1.17 T_1$
$\% \mathbf{increase} = \frac{\mathrm{T}_2 - \mathrm{T}_1}{\mathrm{T}_1} \times 100 = 10\%$
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