{T}_{0} is time period of a simple pendulum at a place. If length of pendulum is reduced to frac{1}{

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13.Oscillations

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${T}_{0}$ is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to $\frac{1}{16}$ times of its initial value, the modified time

A

$8 \pi {T}_{0}$

B

$4 {T}_{0}$

C

${T}_{0}$

D

$\frac{1}{4} T_{0}$

(JEE MAIN-2021)

Solution

Time period of a simple pendulum

${T}_{0}=2 \pi \sqrt{\frac{\ell}{{g}}}$

New time period ${T}=\sqrt[2 \pi]{\frac{\ell / 16}{{g}}}=\frac{2 \pi}{4} \sqrt{\frac{\ell}{{g}}}$

${T}=\frac{{T}_{0}}{4}$

Standard 11

Physics

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