Physics - Gravitation Question with Solution | TestHub

The acceleration due to gravity at a depth $d$ below the Earth's surface is given by $g_d=g(1-\frac{d}{R})$. We are given that $g_d=g/4$. So, $\frac{g}{4}=g(1-\frac{d}{R})$. Dividing by $g$, we get $\frac{1}{4}=1-\frac{d}{R}$. Rearranging the terms, $\frac{d}{R}=1-\frac{1}{4}=\frac{3}{4}$. Therefore, the depth is $d=\frac{3R}{4}$.