QJEEM24Phecbd: JEE Main 2024 Physics - Class 11 JEEM24Phecbd Solution: At what distance above and below the surface of the earth a…

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QJEEM24Phecbd: JEE Main 2024 Physics - Class 11 JEEM24Phecbd Solution: At what distance above and below the surface of the earth a…

At what distance above and below the surface of the earth a body will have same weight. (take radius of earth as $R$ .)

Multiple Choice Options

A 3R−R2
B R2
C 5R−R2
D 5R−R

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Accepted Answer

JEE Main 2024 (Online) 29th January Morning Shift Physics - Gravitation Question 25 English Explanation

$\begin{aligned} g_{p} = \frac{g R^{2}}{(R + h)^{2}} \\ g_{q} = g (1 - \frac{h}{R}) \\ g_{p} = g_{q} \\ \frac{g}{{(1 + \frac{h}{R})}^{2}} = g (1 - \frac{h}{R}) \\ (1 - \frac{h^{2}}{R^{2}}) (1 + \frac{h}{R}) = 1 \end{aligned}$

Take $\frac{h}{R} = x$

So

$\begin{aligned} x^{3} - x + x^{2} = 0 \\ x = \frac{\sqrt{5} - 1}{2} \\ h = \frac{R}{2} (\sqrt{5} - 1) \end{aligned}$

QJEEM24Phecbd: JEE Main 2024 Physics - Class 11 JEEM24Phecbd Solution: At what distance above and below the surface of the earth a…

Multiple Choice Options

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