Question

At what depth below the surface of earth , value of g is same as that at a height 64km above the surface of the earth?

Ans)128km

Answer 1

Below the surface of earth:
g = GM/r2

= G (4/3) π (r3 ρ)/r2
= (4/3)π G (R-d)ρ  -------> (1)

Above the surface of the earth at height h from the center of the earth:

g = G (4/3) π R3 ρ/(R+h)2 -------> (2)

For g to be equal, (1) = (2)
Gives, (R-d)(R+h)2 = R3
Using R = 6371 km, h = 64 km
We get, d = 126.09 km