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 $4 m$ , then the time period of small oscillations will be _________ $s$ .
$[$ take $g = π^{2} m s^{- 2}$ ]

Question

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 $4 m$ , then the time period of small oscillations will be _________ $s$ .

$[$ take $g = π^{2} m s^{- 2}$ ]

TestHub · Accepted Answer

Acceleration due to gravity at surface of earth, $g = \frac{G M}{R^{2}}$ .
Now, at distance $R$ from the surface of the earth, $g^{'} = \frac{G M}{{(R + R)}^{2}} = \frac{g}{4}$
Therefore,
$T = 2 π \sqrt{\frac{l}{\frac{g}{4}}}$
$\Rightarrow T = 2 π \sqrt{\frac{4 \times 4}{g}}$
$\Rightarrow T = 2 π \frac{4}{π} = 8 s$

Physics - SHM Question with Solution | TestHub

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