The change in the value of g at a height h above the surface of the earth is the same as at a depth d below the surface of the earth. When both d and h are much smaller than the radius of the earth, then which one of the following is correct?

Question

Accepted Answer

(1) d=2h. For small height the binomial expansion gives gₕ≈ g(1-(2h)/R), so the change is (2gh)/R. For depth the exact result is g_d=g(1-d/R), so the change is (gd)/R. Equal changes mean (2gh)/R=(gd)/R. So d=2h: you must go twice as deep as you go high to lose the same amount of g.

The change in the value of g at a height h above the surface of the earth is the same as at a depth d below the surface of the earth. When both d and h are much smaller than the radius of the earth, then which one of the following is correct?

Step-by-step solution

Why the other options are wrong