# The center of a 1.00 km diameter spherical pocket of oil

## Homework Statement

The center of a 1.00 km diameter spherical pocket of oil is 1.00 km beneath the Earth's surface[/B]. 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*102 kg/m3

g = G*m/r2

## The Attempt at a Solution

[/B]
Normal gravity = G*m/r2earth
Gravity 0.5 km under the earth = G*m/(rearth-0.5)2
(6378.1/(6378.1-0.5))^2*100 = 100.01
So the gravity increases .01 percent just above the oil.

But the thing concerning me here is that I haven't used the density of oil. Was I supposed to think of it as an extra mass with an effect of G*moil/r2oil? If so, then all I have to is add the magnitude of gravity caused by oil to the normal gravity already being there - 0.5km under the earth, right?

Last edited:

mfb
Mentor
Gravity 0.5 km under the earth
This is both wrong and not relevant.
You cannot use the equation for a point mass if you are inside this mass. And you are supposed to calculate the gravitational force on the surface, not below it.

What is the gravitational force from the oil?
What else changes apart from additional oil?

## Homework Statement

The center of a 1.00 km diameter spherical pocket of oil is 1.00 km beneath the Earth's surface[/B]. 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*102 kg/m3

g = G*m/r2

## The Attempt at a Solution

[/B]
Normal gravity = G*m/r2earth
Gravity 0.5 km under the earth = G*m/(rearth-0.5)2
(6378.1/(6378.1-0.5))^2*100 = 100.01
So the gravity increases .01 percent just above the oil.

But the thing concerning me here is that I haven't used the density of oil. Was I supposed to think of it as an extra mass with an effect of G*moil/r2oil? If so, then all I have to is add the magnitude of gravity caused by oil to the normal gravity already being there - 0.5km under the earth, right?

Were you able to figure this out? I have the exact same question right now and I'm stuck.

mfb
Mentor
Where are you stuck? Do the hints I gave in post #2 (2014...) help?

gneill
Mentor
Were you able to figure this out? I have the exact same question right now and I'm stuck.
What have you tried? Where did you get stuck? You need to show an attempt.