Question

At what altitude will the acceleration due to gravity be $25$% of that at the earth's surface (given radius of earth is $R$)?

• A. $R/4$
• B. $R$
• C. $3R/8$
• D. $R/2$

Answer 1

The correct option is C $3R/8$

$g_h=g(1-\frac{2h}{R})$

Now,

$g_h$ is $25\%$ of $g$

$\therefore g_h=\frac{25}{100}g=\frac{g}{4}$

$\therefore \frac{g}{4}=g(1-\frac{2h}{R})$

So, $h=\frac{3R}{8}$