At what altitude will acceleration due to gravity be 25% of that at earth’s surface (given rad

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7.Gravitation

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

A

$R/4$

B

$R$

C

$3R/8$

D

$R/2$

Solution

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

$g_{h}=\frac{G M}{(R+h)^{2}} \dots(2)$

$\frac{g_{h}}{g_{0}}=\left(\frac{R}{R+h}\right)^{2} \Rightarrow \frac{1}{4}=\left(\frac{R}{R+h}\right)^{2}$

$\frac{R}{R+h}=\frac{1}{2}$

$R+h=2 R \Rightarrow h=R$

Standard 11

Physics

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