At what height from surface of earth the value of acceleration due to gravity will fall to half that on the surface of the earth?

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Aicharya · Accepted Answer

If $g$ be the gravitational acceleration on the surface of earth, then gravitational acceleration at height $h$ given as $\begin{aligned} & g_h=\frac{g}{\left(1+\frac{h}{R_e}\right)^2} \ & \text{But, } g_h=\frac{g}{2} \ & \therefore \quad \frac{g}{2}=\frac{g}{\left(1+\frac{h}{R_e}\right)^2} \ & \Rightarrow \quad\left(1+\frac{h}{R_e}\right)^2=2 \ & \Rightarrow \quad 1+\frac{h}{R_e}=\sqrt{2} \ & \Rightarrow \quad h=(\sqrt{2}-1) R_e \ & =(1.414-1) 6400 \ & =2649.6 \mathrm{~km} \ & \simeq 2625 \mathrm{~km} \ \end{aligned}$

At what height from surface of earth the value of acceleration due to gravity will fall to half that on the…

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