(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

3. 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

g_{h}= GM/(R+h)^{2}

After adding R^{2}to both denominator and numerator, we get the formula

g_{h}= 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 'g_{h}' will actually increase, which is not the case. I know that the correct formula to be used here is g_{h}= 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.

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# What is the derivation for decrease in g with depth?

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