Gravity and Radius of the earth problem

[J.Sterling47]

Homework Statement

Hey guys, I have a problem where we measured the gravity on separate floors of a building using a gravometer. It gave us values in mgals. So each floor has a distance of 0.5m. How do we take this into account as we move up and down the floors? As we move up, there's and increase of mass below us and vice versa as we go down. The goal is to calculate the radius of the Earth using this method.

Homework Equations

dg/g = -2(dr/r) where dg is the change in gravity per floor and dr is the height of each floor. We got the radius to be close at about 6500km, but without taking into account the changing of the mass below.

The Attempt at a Solution

Don't really know where to start

 

[DaveC426913]

So each floor has a distance of 0.5m.

You sure about that?

 

[J.Sterling47]

You sure about that?

Yeah sorry it was supposed to be 5m. I converted it wrong but yea

 

[haruspex]

We got the radius to be close at about 6500km, but without taking into account the changing of the mass below.

If you are concerned about that, the first thing is to get an upper bound on how much difference that will make. Estimate the mass per floor of the building. Be generous. Likewise, maximise the effect by assuming all that extra mass is only one floor below (for simplicity). How much difference will that make to your answer?