Question

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

Answer 1

The correct option is C .$d=2h$

The value of gravity at a height $h$ above earth's surface is given by
$g_h=g(1-\frac{2h}{R})$
and at a depth $d$ is given by
$g_d=g(1-\frac{d}{R})$
Since these two values are same, we can see that $d=2h$