What happens when you reach the centre of gravity?

If someone was to (hypothetically) create a hole through the center of the earth or any planet big enough to have a strong gravitational pull, what would happen if you jumped? First you would fall but when you reached the center the gravity would be pulling the other way right? I tried asking both of my physics teachers this question but they both dismissed it as a stupid question and if you drilled through the earth you would reach boiling hot magma and blah blah blah. I know. But if there wasn't what would happen?