Question

At what height above the surface of the Earth, the value of acceleration due to gravity is the same as in a mine 200 km deep?
1. 200 km
2. 150 km
3. 100 km
4. 50 km

Answer 1

Correct Answer - Option 3 : 100 km

Given,

Depth = d = 200 km

To find height (h)

We know,

At height h from the surface of the Earth, the value of acceleration due to gravity = \(g'_h=g(1-\frac{2h}{R})\)

At depth d from the surface of the Earth, the value of acceleration due to gravity = \(g'_d=g(1-\frac{d}{R})\)

Here R is the radius of the Earth

According to the question,

\(g'_h=g'_d\\ or, \; g(1-\frac{2h}{R})=g(1-\frac{d}{R})\\ or, \; \frac{2h}{R}=\frac{d}{R}\\ or, \; h=\frac{d}{2}=\frac{200}{2}=100 \; km\)