Question

The change in the value of '$g$' at a height '$h$' above the surface of the earth is the same as at a depth '$d$' below the surface of earth. When both '$d$' and '$h$' are much smaller than the radius of earth, then which one of the following is correct ?

• A. $d=\frac{h}{2}$
• B. $d=\frac{3h}{2}$
• C. $d=2\,h$
• D. $d=h$

Answer 1

Answer: (C)

$g_{h}=g\left(1-\frac{2\,h}{R}\right)\,...\left(i\right)$
$g_{d}=g\left(1-\frac{d}{R}\right)\,...\left(ii\right)$
From Eqs. $\left(i\right)$ and $\left(ii\right)$,
$g\left(1-\frac{2\,h}{R}\right)=g\left(1-\frac{d}{R}\right)$
$\Rightarrow 2\,h=d$