Question

At what depth from the surface of the earth (in terms of the radius of earth) the acceleration due to gravity will be $\frac{2g}{5}$
(correct answer + 1, wrong answer - 0.25)

• A. $\frac{2}{5}R$
• B. $\frac{3}{5}R$
• C. $\frac{4}{25}R$
• D. $\frac{9}{25}R$

Answer 1

The correct option is B $\frac{3}{5}R$

Gravity due to the earth at depth is $g^{\prime }=g(1-\frac{d}{R})$
Where d = depth from the surface of the earth, R = radius of the earth,
Given that $g^{\prime }=\frac{2g}{5}$
$\Rightarrow \frac{2g}{5}=g(1-\frac{d}{R})$
$\frac{2}{5}=[1-\frac{d}{R}]\Rightarrow \frac{d}{R}=1-\frac{2}{5}$
$\Rightarrow \frac{d}{R}=\frac{3}{5}$