When searching for gold, measurements of g can be used find regions within the Earth where the density is larger than that of normal soil. Such measurements can also be used to find regions in which the density of the Earth is smaller than normal soil; such regions might contain a valuable fluid (oil). Consider a deposit of oil that is 380 m in diameter and just below the surface of the Earth. For simplicity, assume the deposit is spherical. Estimate the change in the magnitude of the acceleration due to gravity on the surface above this deposit. Assume that the density of the oil is 1320 kg/m3 and the density of normal soil and rock is 2260 kg/m3. Note: Companies that search for valuable minerals actually use this method.

Question

When searching for gold, measurements of g can be used find regions within the Earth where the density is larger than that of normal soil. Such measurements can also be used to find regions in which the density of the Earth is smaller than normal soil; such regions might contain a valuable fluid (oil). Consider a deposit of oil that is 380 m in diameter and just below the surface of the Earth. For simplicity, assume the deposit is spherical. Estimate the change in the magnitude of the acceleration due to gravity on the surface above this deposit. Assume that the density of the oil is 1320 kg/m3 and the density of normal soil and rock is 2260 kg/m3. Note: Companies that search for valuable minerals actually use this method.

Answer 1

There is no answer

Answer 2

To estimate the change in the magnitude of the acceleration due to gravity above the oil deposit, we need to calculate the gravitational attraction between the deposit and a point on the Earth's surface.

Here are the steps to determine the change in acceleration due to gravity:

1. Calculate the volume of the oil deposit:
Volume = (4/3) * π * (radius)^3
Since the diameter is given, the radius will be half the diameter.
Volume = (4/3) * π * (190 m)^3

2. Calculate the mass of the oil deposit:
Mass = Density * Volume
Mass = 1320 kg/m^3 * Volume

3. Calculate the mass of the equivalent volume of normal soil and rock:
Mass_normal = Density_normal * Volume
Mass_normal = 2260 kg/m^3 * Volume

4. Calculate the difference in mass between the oil and normal soil/rock:
Mass_difference = Mass - Mass_normal

5. Calculate the gravitational force between the oil deposit and a point on the surface:
Gravitational force = G * (Mass_difference) / (distance)^2
The distance here is the radius of the Earth (assuming the deposit is just below the surface).

6. Calculate the change in acceleration due to gravity:
Change in acceleration = Gravitational force / (mass of the test object)
In this case, the mass of the test object is negligible compared to the mass of the Earth, so we can assume it to be zero.

By following these calculations, you can estimate the change in the magnitude of the acceleration due to gravity above the oil deposit.