You may not find this helpful, but...
As part of your course, have you written down a formula for the field strength at the surface of a planet in terms of the density and radius of the planet? If so, you can use that here.
The trick is to realize that the strength of the gravitational field decreases as you approach the centre of the planet and and the centre is zero. If you think about what it would be like to be surrounded by a large uniform shell of matter - pulled equally in all directions - you will see that this is true.
It turns out that when we go 'down' the tunnel into the planet we only have to worry about the mass that's enclosed by the sphere that is closer to the middle than we are. We've assumed that the planet is of uniform density so this is just like standing on the surface of a new, smaller planet. This is where your equation for g in terms of ρ and r comes in handy. You can write down an equation showing how g changes with r. Remember that g is the same as the acceleration? By thinking about the form of your equation you should recognise that this will cause a special kind of motion. Once you spot this, answering the question is easy.
Alternatively, you could just look up what the potential energy would be in the middle of a planet and find the difference between that value and the PE on the surface.