Question

At what height from the surface of the earth (in terms of the radius of earth) the acceleration due to gravity will be $\frac{4g}{9}?$

• A. $9R/4$
• B. $R/2$
• C. $3R/2$
• D. $4R/9$

Answer 1

The correct option is B $R/2$

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

$g_h=\frac{4g}{9}$

$\therefore \frac{4g}{9}=\frac{g}{{(1+\frac{h}{R})}^2}\Rightarrow 2(1+\frac{h}{R})=3$

$\Rightarrow 1+\frac{h}{R}=\frac{3}{2}$

$\frac{h}{R}=\frac{3}{2}-1=\frac{1}{2}$

or, $h=\frac{R}{2}$