Question

The change in the value of $g$ at a height $h$ about 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. $d=h$
• B. $d=2h$
• C. $d=\frac{3h}{2}$
• D. $d=\frac{h}{2}$

Answer 1

Answer: (B)

$d=2h$

Acceleration due to gravity at a height $h$, $g_h^{\prime }=g(1-\frac{2h}{R})$
Acceleration due to gravity at a depth $d$, $g_d^{\prime }=g(1-\frac{d}{R})$
$\therefore g(1-\frac{2h}{R})$ $=g(1-\frac{d}{R})$
or $\frac{2h}{R}=\frac{d}{R}$
or $d=2h$.