Question

Let $g_h$ and $g_d$ be the acceleration due to gravity at height h above the earth's surface and at depth d below the earth's surface respectively. If $g_h=g_d$, then the relation between h and d is

• A. $d=h$
• B. $d=\frac{h}{2}$
• C. $d=\frac{h}{4}$
• D. $d=2h$

Answer 1

The correct option is D $d=2h$

Let the radius of the earth be $R$ and acceleration due to gravity at earth surface be $g$.

Acceleration due to gravity at height $h$ above the earth surface, $g_h=g(1-\frac{2h}{R})$

Acceleration due to gravity at depth $d$ below the earth surface, $g_d=g(1-\frac{d}{R})$

Now for $g_h=g_d$ we get, $g(1-\frac{2h}{R})$ $=g(1-\frac{d}{R})$

$\Rightarrow$ $1-\frac{2h}{R}=1-\frac{d}{R}$

$\Rightarrow$ $d=2h$