Calculating Energy Ratios: Moving Mass to and from Earth's Core

[arella]

Homework Statement

Hi all, I've tried both a and b and I keep getting "The force is not constant, so it's not correct just to say that work is just the product of force and displacement." and "How is g related to G, M, and R?" respectively. I'm not sure where to go from here!

Relevant Equations

gr/R

a) In the rough approximation that the density of the Earth is uniform throughout its interior, the gravitational field strength (force per unit mass) inside the Earth at a distance r from the center is gr/R, where R is the radius of the Earth. (In actual fact, the outer layers of rock have lower density than the inner core of molten iron.) Using the uniform-density approximation, find an expression for the amount of energy required to move a mass m from the center of the Earth to the surface.

b) Calculate the ratio of the energy you found, to the energy required to move the mass from Earth's surface to a very large distance away. (Your answer should be a pure number.)

 

[haruspex]

You can suppose the force is approximately constant over a very short distance, dr. What energy is required to raise the mass from radius r to radius r+dr.
Does that give you a clue?

 

[mfb]

Hi all, I've tried both a and b and I keep getting "The force is not constant, so it's not correct just to say that work is just the product of force and displacement." and "How is g related to G, M, and R?" respectively. I'm not sure where to go from here!

Please show what you did, otherwise it's impossible to tell where you made a mistake.