Physics - Gravitation Question with Solution | TestHub

The acceleration due to gravity at the surface of the earth is $g=\frac{GM}{R^2}$

The acceleration due to gravity at a height $h$ above the surface is $g_h=\frac{GM}{(R+h{)}^2}$

Given that $g_h=\frac{g}{n}$

Substituting the expressions for $g$ and $g_h$:

$\frac{GM}{(R+h{)}^2}=\frac{1}{n}\frac{GM}{R^2}$

$(R+h{)}^2=n{R}^2$

Taking the square root on both sides:

$R+h=\sqrt{n}R$

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

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