Gravity

[envscigrl]

Problem:
Calculate the distance from the center of the Earth to a point below the surface where the acceleration due to gravity is 0.50g, where g is the acceleration due to gravity at the Earth's surface.
I thougtt I could use g = GMe / R^2 solving for R. But this did not work.
This problem seems really simple I just cant seem to figure it out.

[Doc Al]

I thougtt I could use g = GMe / R^2 solving for R.
That equation is only good for points at or above the earth's surface. You need to figure out the force of gravity beneath the surface, for r < Re. Hint: treat the earth as a sphere of uniform density. The gravity experienced at any given distance from the center r depends only on the mass located beneath that point (the force from the shell of mass above the point cancels out).