Question

The light vertically above the earth's surface at which the acceleration due to gravity becomes $1\%$ of its value at the surface is ___?

(R is the radius of the earth)

• A. $8R$
• B. $9R$
• C. $10R$
• D. $20R$

Answer 1

The correct option is B $9R$

The acceleration due to gravity varies with height as

$g^{\prime }=\frac{g}{{\left(\begin{array}{c}1+\frac{h}{R}\end{array}\right)}^2}$

$\Rightarrow \frac{g}{100}=\frac{g}{{\left(\begin{array}{c}1+\frac{h}{R}\end{array}\right)}^2}$

$\Rightarrow {\left(\begin{array}{c}1+\frac{h}{R}\end{array}\right)}^2=100$

$\Rightarrow h=9R$