Question

The acceleration due to gravity at a height $1\, km$ above the earth is the same as at a depth $d$ below the surface of earth. Then :

• A. $d = 1 km$
• B. $d = \frac{3}{2} km$
• C. $d = 2 k m$
• D. $d = \frac{1}{2} km$

Answer 1

Answer: (C)

$d = 2 k m$

Answer 2

Above earth surface
$g'=g\left(1-\frac{2 h}{R_{e}}\right)$
$\Delta g'=g \frac{2 h}{R_{e}}$...(1)
From (1) & (2)
$d=2 h$
$d=2 \times 1\, km$
Below earth surface
$g'=g\left(1-\frac{d}{R_{e}}\right)$
$\Delta g=g \frac{d}{R_{e}}$...(2)