Question

At what height from the surface of the earth (in terms of the radius of earth) the acceleration due to gravity will be $\frac{g}{100}?$

• A. $10R$
• B. $9R$
• C. $100R$
• D. $R/100$

Answer 1

The correct option is B $9R$

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

$g_h=\frac{g}{100}$

$\therefore \frac{g}{100}=\frac{g}{{(1+\frac{h}{R})}^2}\Rightarrow \frac{1}{100}=\frac{1}{{(1+\frac{h}{R})}^2}$

$100={(1+\frac{h}{R})}^2\Rightarrow 10=1+\frac{h}{R}$

or, $h=9R$