Physics Problem Involving Gravitational Force on an object based on R

1. Nov 20, 2013

taylorkrauss

1. The problem statement, all variables and given/known data

At what distance r inside the Earth is the gravitational force due to Earth the same as at
the distance r = 4RE (where the latter distance is clearly outside Earth)? Assume uniform
density of Earth.

2. Relevant equations

conservation of energy? TME = GPE + KE

3. The attempt at a solution

At first I thought I could do conservation of energy and set both GPE's equal to each other and solve for a new Radius, but this is not working out well. Is there something I need to do involving the density of Earth and the mass? I really have no idea. Thanks for any help!

2. Nov 20, 2013

Pythagorean

Energy conservation doesn't appear relevant to me... I'd go with Gauss.

3. Nov 20, 2013

taylorkrauss

Hmm...I haven't learned Gauss's Law though. This wants Gravitational Force and Gravitational Potential not Electric Force and EPE, so I'm not sure how I'd apply Gauss (after googling, I saw it was a theroem for electric potential). How would you go about using Gauss's Law?

4. Nov 20, 2013

Pythagorean

5. Nov 20, 2013

taylorkrauss

That was perfect! Thank you!