Question

At what height (in terms of radius of earth) the acceleration due to gravity will be:
(a) $\frac{g}{2}$ (b) $\frac{4g}{9}$ (c) $\frac{g}{100}$

Answer 1

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

(a) $\frac{g}{2}=\frac{g{R}^2}{(R+h{)}^2}$
$(R+h{)}^2=2R^2$
$(R+h)=\sqrt{2}R$
$h=R(\sqrt{2}-1)$

(b) $\frac{4g}{9}=\frac{g{R}^2}{(R+h{)}^2}$
$4(R+h{)}^2=9R^2$
$2(R+h)=3R;h=R/2$

(c) $\frac{g}{100}=\frac{g{R}^2}{(R+h{)}^2}$
$(R+h{)}^2=100R^2$
$(R+h)=10R$
$h=9R$