Question

At what height from the surface of the earth (in terms of the radius of earth) the acceleration due to gravity will be $\frac{g}{2}?$

• A. $R\sqrt{2}$
• B. $R(\sqrt{2}-1)$
• C. $R$
• D. $R(\sqrt{2}-2)$

Answer 1

The correct option is B $R(\sqrt{2}-1)$

We have, $g_h=\frac{g}{{(1+\frac{h}{R})}^2}$

$g_h=\frac{g}{2}$

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

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

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

$1+\frac{h}{R}=\sqrt{2}$

$\frac{h}{R}=\sqrt{2}-1$

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