Find the Volume of an Oil Deposit

[nzashadow]

Homework Statement

A geologist searching for oil finds that the gravity at a certain location is 5 parts in 10^7 smaller than average. Assume that a deposit of oil is located 2000 meters directly below.

Estimate the size of the deposit, assumed spherical. Take the density (mass per unit volume) of rock to be 3000 kg/m^3 and that of oil to be 800 kg/m^3.

Homework Equations

g = F/m ...?

The Attempt at a Solution

Usually when trying to do physics homework, I try to build the solution without following the book, or looking up equations, based on my understanding of how the concepts work out.

My first thought was to find the radius of the oil deposit... however I could see no way to figure that out. My second thought, and my first approach, was to cube the distance, and turn it into a ratio problem. However several attempts an reattempts just did not seem to work. After a long while I did consult the book, which had no examples that I could see related to the problem.

I did find one equation that seems like it could be applied to the situation, however I cannot seem to figure out how to apply it. This equation being g = F/m.

 

[ehild]

Use the Universal law of gravity, F=GmM/r², the force between two point masses m and M at distance r. A homogeneous sphere can be considered as a point mass in the centre of the sphere. The Earth can be considered so, but it has the oil deposit with less density than that of the Earth. You can handle the problem that you have the Earth, and the oil deposit, an other sphere, with centre 2000 m from the surface, where the material of the Earth is missing, and is filled with a lower density material, so having negative density: ρ=ρ(oil)-ρ(earth). The resultant of the gravitational forces of both spheres on unit mass is the gravitational force measured. So the difference from the average gravity is equal to the gravity of a sphere with density ρ=ρ(oil)-ρ(earth).

ehild