Question

At what height above the surface of earth the value of $g$ decreases by $2\%$ ?
$($radius of the earth is $6400\text{km})$

• A. $32\text{km}$
• B. $64\text{km}$
• C. $128\text{km}$
• D. $1600\text{km}$

Answer 1

The correct option is B $64\text{km}$

Acceleration due to gravity above the surface of earth at a height $h$ is $g^{\prime }$ which is given as

$g^{\prime }=g(1-\frac{2h}{R_e})$

Here, $g^{\prime }=0.98g$

$\Rightarrow 0.98g=g(1-\frac{2h}{R_e})$

$\Rightarrow 0.98=(1-\frac{2h}{R_e})$

$\Rightarrow \frac{2h}{R_e}=0.02\Rightarrow h=0.01R_e=0.01\times 6400$

$\Rightarrow h=64\text{km}$

Therefore, option $\left(b\right)$ is correct.

Why this question? Caution - This result can be used only when $h<<R$.