A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is $4 \mathrm{~m}$, then the time period of small oscillations will be ____ $s$. $\left[\right.$ take $\left.\mathrm{g}=\pi^2 \mathrm{~ms}^{-2}\right]$
JEE MAIN 2024, Diffcult
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Acceleration due to gravity $\mathrm{g}^{\prime}=\frac{\mathrm{g}}{4}$
$T=2 \pi \sqrt{\frac{4 \ell}{g}}$
$T=2 \pi \sqrt{\frac{4 \times 4}{g}}$
$T=2 \pi \frac{4}{\pi}=8 s$
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