Gravitation (Preliminary Reference Earth Model)

[ceomtcl]

Homework Statement

Assuming that we know the density of Earth as a function of radius, we have to derive the equation for gravity as the function of radius.

Homework Equations

The Attempt at a Solution

lets us choose density as $$\rho$$(r).
I know that within a hollow sphere there is no gravity.
We can assume sum of several hollow spheres with thickness dr, where r is the radius of the shell from center, and then we can integrate it.
I know its an easy question we used to do in undergraduate study, but I am missing something and i can't figure out how it was done? Please help!

 

[Redbelly98]

Hint: what is the volume of a hollow sphere, radius=r, thickness=dr?

Given the volume and density, what would be it's mass?

 

[ceomtcl]

Thanks Redbelly98!

I did this problem. However I am having another problem in an associated problem with this question. I am working it out, however if I get stuck then i would ask you to help me.

Thanks once again!