Question

At what depth from the surface of the earth (in terms of the radius of earth) the acceleration due to gravity will be: $\frac{2g}{5}$?

• A. $2/5R$
• B. $3/5R$
• C. $4/25R$
• D. $9/25R$

Answer 1

The correct option is B $3/5R$

Gravity due to the earth is at depth $g$'=$g(1-\frac{d}{R})$,

Where $d$= depth from the surface of the earth, $R$= Radius of the earth,

Given that $g$'= $\frac{2g}{5}$

$\Rightarrow \frac{2g}{5}=g(1-\frac{d}{R})$,

Solving this $\Rightarrow d=\frac{3}{5}R$