Physics - Gravitation Question with Solution | TestHub

The acceleration due to gravity at a height $h$ above the earth's surface is given by

$g_h=\frac{g}{{\left(1+\frac{h}{R}\right)}^2}$

Given that $g_h=\frac{g}{3}$, substituting this in the formula gives

$\frac{g}{3}=\frac{g}{{\left(1+\frac{h}{R}\right)}^2}$

${\left(1+\frac{h}{R}\right)}^2=3$

Taking the square root on both sides,

$1+\frac{h}{R}=\sqrt{3}$

$\frac{h}{R}=\sqrt{3}-1$

$h=(\sqrt{3}-1)R$

Answer: $(\sqrt{3}-1)R$