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 the earth. When both $d$ and $h$ are much smaller than the radius of earth, then which one of the following is correct?

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

Answer 1

The correct option is D $d=2h$

Variation of $g$ with altitude $h$ is given by

$g_h=g[1-\frac{2h}{R}](\because h<<R)$

Also, variation of $g$ with depth $d$ is given as

$g_d=g[1-\frac{d}{R}](\because d<<R)$

Equating $g_h$ and $g_d$, we get

$d=2h$

Hence, option $\left(d\right)$ is correct.

Why this question? Tip: The result $g_d=g(1-\frac{d}{R})$ is valid for any value of $d$, small or large.