At what altitude will the acceleration due to | vedclass

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Question

$g=\frac{G M}{r^{2}} \Rightarrow g_{0}=\frac{G M}{R^{2}} \ldots(1)$

$g_{h}=\frac{G M}{(R+h)^{2}} \dots(2)$

$\frac{g_{h}}{g_{0}}=\left(\frac{R}{R

Vedclass · Accepted Answer

$R$

Vedclass · Answer

$g=\frac{G M}{r^{2}} \Rightarrow g_{0}=\frac{G M}{R^{2}} \ldots(1)$

$g_{h}=\frac{G M}{(R+h)^{2}} \dots(2)$

$\frac{g_{h}}{g_{0}}=\left(\frac{R}{R+h}\right)^{2} \Rightarrow \frac{1}{4}=\left(\frac{R}{R+h}\right)^{2}$

$\frac{R}{R+h}=\frac{1}{2}$

$R+h=2 R \Rightarrow h=R$

At what altitude will the acceleration due to gravity be $25\% $ of that at the earth’s surface (given radius of earth is $R$) ?

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