physics
posted by fatima on .
If the change in the value of 'g ' at a height 'h ' above the surface of earth is the same as at a depth 'x ' below it. When both x and h are much smaller than the radius of the earth. The relation between x and h is?

g = GM/r^2
at r+h, g1 = GM/(r+h)^2
at rx, g2 = GM/(rx)62
∆g = GM(1/(rx)^2  1/(r+h)^2)
= GM/((rx)^2(r+h)^2) ((r+h)^2(rx)^2)
= GM/((rx)^2(r+h)^2) (2rh+h^2  2rx+x^2)
Since rx and r+h are both approximately r, we have
∆g = GM/r^4 (2r(hx) + h^2+r^2)
= 2GM/r^3 (hx)
The h^2+r^2/r^4 is negligible.
hx = r^3∆g/GM
Not sure just what kind of answer you want.