Question

The height of the point vertically above the earth's surface at which acceleration due to gravity becomes $1$% of its value at the surface of earth is
$(R=$ radius of earth$)$

• A. $8R$
• B. $9R$
• C. $7R$
• D. $6R$

Answer 1

The correct option is B $9R$

The variation of $g$ with height is given by,

$g^{\prime }={\left(\frac{R}{R+h}\right)}^{2}g$
$\Rightarrow \frac{1}{100}g={\left(\frac{R}{R+h}\right)}^{2}g$
$\Rightarrow \frac{1}{10}=\frac{R}{R+h}$
$\Rightarrow 10R=R+h$
$\Rightarrow h=9R$