We know that 'g' decreases with height and the derivation for the formula is straight enough, but how is the formula for decrease of 'g' with depth derived?
The Attempt at a Solution
If an object is taken to a height 'h' above the surface of the earth and assuming the radius of the earth as 'R', then acceleration due to gravity at a height 'h' is given by the formula
gh = GM/(R+h)2
After adding R2 to both denominator and numerator, we get the formula
gh = g[R/(R+h)]2
However, the same formula will not work for depth because if (R-h) is substituted for (R+h) in the above formula, then the value of 'gh' will actually increase, which is not the case. I know that the correct formula to be used here is gh = g[(R-h)/R], but how is that derived ? I know this is pretty basic but I am not able to get the hang of it.
Would appreciate if somebody can please explain.