Gravity problem - change in g due to oil pocket

[deuce123]

Homework Statement

The center of a 1.40 km diameter spherical pocket of oil is 1.40 km beneath the Earth's surface.

Estimate by what percentage g directly above the pocket of oil would differ from the expected value of g for a uniform Earth? Assume the density of oil is 8.0×102kg/m3.

Homework Equations

F=(m1m2G)/r^2

The Attempt at a Solution

I got the mass for the pocket of oil, then subtracted the distance its beneath the Earth from the Earth's radius for the length, I ended up getting F=1.1x10^13N, and from here on I'm lost. I divided that number by the oils mass (1.12x10^12kg) and got a number close to g, then got a percentage for the difference, but it's still incorrect. Someone please tell me what I'm doing wrong. Thank you.

 

[haruspex]

subtracted the distance its beneath the Earth from the Earth's radius for the length,

Length of what?

Can you calculate the attraction you should feel (at the surface) towards the sphere of oil?
Note that it says "uniform Earth". I.e. you are to pretend the Earth has uniform density, apart from the oil pocket.
On that basis, what would be the gravitational attraction to the sphere of Earth that the oil has replaced?

 

[deuce123]

Length of what?

Can you calculate the attraction you should feel (at the surface) towards the sphere of oil?
Note that it says "uniform Earth". I.e. you are to pretend the Earth has uniform density, apart from the oil pocket.
On that basis, what would be the gravitational attraction to the sphere of Earth that the oil has replaced?

I'm confused as too what you mean, do you mean calculate the attraction between the sphere of oil and Earth if it were at Earth's surface? And for the second part you mean consider the sphere of oil as a part of the mass of earth? ( remove a portion of the Earth of same size and get the total change in mass??) Can you also explain why the method I use did not work out, I'm interested as too why it didn't work. And for L I mean the length from the center of the Earth to the center of the sphere of oil

 

[haruspex]

do you mean calculate the attraction between the sphere of oil and Earth if it were at Earth's surface?

No. Consider an object on the surface of the Earth, directly above the oil pocket. What gravitational attraction, (as an acceleration) does the oil pocket have for the object? In this part, ignore the Earth.

for the second part you mean consider the sphere of oil as a part of the mass of earth?

No. As in the first part, I am asking about the attraction towards the pocket. But in this case, consider the pocket as occupied by earth, not by oil.

for L I mean the length from the center of the Earth to the center of the sphere of oil

Why is that interesting? What equation did you plug that into and on what basis?