Question

At what height, is the value of $g$ half that on the surface of earth? ($R=$ radius of the earth)

• A. $0.414R$
• B. $R$
• C. $2R$
• D. $3.5R$

Answer 1

The correct option is A $0.414R$

$g{}^{\prime }=\frac{{gR}^2}{r^2}=\frac{g}{2}\Rightarrow r^2={2R}^2\Rightarrow r=R\sqrt{2}=R+h\Rightarrow h=R(\sqrt{2}-1)=R(1.414-1)=0.414R$