Question

At what depth below the surface of the earth, the value of $g$ is the same as that at a height of $5km$ ?

• A. 1.25 km
• B. 2.5 km
• C. 5 km
• D. 7.5 km
• E. 10km

Answer 1

Answer: (E)

Acceleration due to gravity at the surface of earth
$g_h=g{\left(1+\frac{h}{R}\right)}^{-2}$
$g_h=g\left(g-\frac{2h}{R}\right)$
Acceleration due to gravity at depth d from the surface of the earth
$g_d=g\left(1-\frac{d}{R}\right)$
Given: $g_h=g_d$
$\therefore$ $\frac{2h}{R}=\frac{d}{R}$
Or $d=2h$ Or $d=10km$