Find the height over the earth's surface at which the weight of a body becomes half of its value at

Question

Find the height over the earth's surface at which the weight of a body becomes half of its value at the surface. (Let $R$ be the radius of the earth)

Professor PC Thomas Classes · Answer

$g' = \frac{g}{(1+h/R)^2}$. For $g' = g/2$, $(1+h/R)^2 = 2 \implies h = (\sqrt{2}-1)R$.