T is time period of simple pendulum on earth's surface. Its time period becomes x T when taken t

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7.Gravitation

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$T$ is the time period of simple pendulum on the earth's surface. Its time period becomes $x T$ when taken to a height $R$ (equal to earth's radius) above the earth's surface. Then, the value of $x$ will be:

A

$4$

B

$2$

C

$\frac{1}{2}$

D

$\frac{1}{4}$

(JEE MAIN-2023)

Solution

At surface of earth time period

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

At height $h = R$

$g ^{\prime}=\frac{ g }{\left(1+\frac{ h }{ R }\right)^2}=\frac{ g }{4}$

$xT =2 \pi \sqrt{\frac{\ell}{( g / 4)}}$

$\Rightarrow xT =2 \times 2 \pi \sqrt{\frac{\ell}{ g }}$

$\Rightarrow xT =2 T \Rightarrow x =2$

Standard 11

Physics

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