Question

At what depth below the earth surface is the acceleration due to gravity the same as at a given height?

Answer 1

Dear Student,

Let the height be given, h
g at height h will be $g_h=g(1-\frac{2h}{R})$

g at depth d will be $g_d=g(1-\frac{d}{R})$

Given, at depth d, $g_d=g(1-\frac{d}{R})$ = $g_h=g(1-\frac{2h}{R})$
$$\begin{gathered} \Rightarrow g(1-\frac{d}{R})=g(1-\frac{2h}{R}) \\ \Rightarrow d=\frac{2hg}{R} \end{gathered}$$

Regards