Physics - Gravitation Question with Solution | TestHub

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

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

Given that $g^{\prime }=\frac{g}{2}$

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

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

$R+h=\sqrt{2}R$

$h=(\sqrt{2}-1)R$

Answer: $(\sqrt{2}-1)R$