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  4. The approximate height from the surface of earth at which the weight of the body becomes (1/3) of its weight on the surface of earth is: [Radius of earth R =6400 km and √3=1.732]

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Q. The approximate height from the surface of earth at which the weight of the body becomes $\frac{1}{3}$ of its weight on the surface of earth is :
[Radius of earth $R =6400\, km$ and $\sqrt{3}=1.732]$

JEE MainJEE Main 2022Gravitation

Solution:

$Mg ^{\prime}=\frac{ M }{3} g$
$g ^{\prime}=\frac{ g }{3}$
$g ^{\prime}= g \left(\frac{ R }{ R + h }\right)^{2}=\frac{ g }{3}$
$\frac{ R }{ R + h }=\frac{1}{\sqrt{3}}$
$h =(\sqrt{3}-1) R$
$=(1.732-1) 6400$
$h =4685 \,km$