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

Answer 1

Answer: (A)

The correct option is A $d=2km$
Acceteration due to gravity at height h,
$g_n=g_0(1-\frac{2h}{R})$ $h=1km$
Acceleration due to gravity at depth d,
$d_d=g_0(1-\frac{d}{R})$
$g_h=g_d$
$g_0(1-\frac{2h}{R})=g_0(1-\frac{d}{R})$
$\to d=2h$
$=2\times 1km$
$d=2km$