Question

How far away from the earth does the acceleration due to gravity become $10\%$ of its value on earth's surface? Radius of earth $=6.37\times {10}^6$m.

Answer 1

$g_R=\frac{g{R}^2}{{(R+h)}^2}-\left(i\right)g_R=\frac{10}{100}g-\left(ii\right)\left(i\right)=\left(ii\right)\Rightarrow \frac{g}{10}=\frac{g\times R^2}{{(R+h)}^2}\Rightarrow {(R+h)}^2=10R^2\Rightarrow R+h=\sqrt{10}\times R\Rightarrow h=(\sqrt{10}-1)R=1.38\times {10}^{7}m$