Physics Problem Involving Gravitational Force on an object based on R

[taylorkrauss]

Homework Statement

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.

Homework Equations

conservation of energy? TME = GPE + KE

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!

 

[Pythagorean]

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

 

[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?

 

[Pythagorean]

Hrm... maybe you can use this then...

http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/earthole.html

 

[taylorkrauss]

That was perfect! Thank you!