Question

How far away from the surface of the earth does the acceleration due to gravity becomes $4\%$ of its value on the surface of earth?$[R_e=6400km]$
Hint: $g_1=g[\frac{R}{R+h}{]}^2$

Answer 1

Acceleration due to gravity $g^{\prime }=\frac{4}{100}{g}_s$

Using $g^{\prime }=g_s[\frac{R}{R+h}{]}^2$

Or $\frac{4}{100}{g}_s=g_s[\frac{R}{R+h}{]}^2$

Or $\frac{R}{R+h}=\frac{2}{10}$

$⟹h=4R=4\times 6400=25600km$