[Former Fetus]

I asked this question years ago, as an extra credit question, in a Physics test. I asked the students to consider only the effect of the gravity. More than half answered that “you would fall out the bottom of the hole”, while other answers ranged from “you would not fall into the hole if the tunnel was dug parallel to the equator” to “who cares?” As the Physics teacher, it was a very humbling moment.

[amihow]

How do we know that atmosphere plays no part in falling, only mass below?

[IronJack]

You would achieve enough momentum to carry you past the point of zero gravity (the center), so that you would "fall upward" for a ways. Then you would lose the momentum and fall back, with slightly less energy until you passed the center going the other way, then you would oscillate back and forth before eventually coming to a stop at the equilibrium point -- the center.

I asked this same question to a physics instructor when I was going to college.