Physics - Gravitation Question with Solution | TestHub

The acceleration due to gravity at a depth $d$ below the surface of the earth is given by:

$g_d=g\left(1-\frac{d}{R}\right)$

Given that the value of acceleration due to gravity at depth $d$ is $\frac{1}{n}$ times the value at the surface:

$g_d=\frac{g}{n}$

Equating the two expressions:

$\frac{g}{n}=g\left(1-\frac{d}{R}\right)$

$\frac{1}{n}=1-\frac{d}{R}$

Rearranging the terms to solve for $d$:

$\frac{d}{R}=1-\frac{1}{n}$

$\frac{d}{R}=\frac{n-1}{n}$

$d=\frac{R(n-1)}{n}$

Answer: $\frac{R(n-1)}{n}$