If you dig a hole from the top of earth through the bottom, what would happen?

Theoretically no!When you fall into a 'normal' hole you'd just keep on picking up speed until you reached your maximum velocity or hit the bottom. If this hole goes all the way through the earth, you'd think that you'd fly out the other end like a cannonball but no, this wouldn't happen. The reason you keep falling in a normal hole is that gravity is continuing to pull you in the direction of the earth’s center. In your imaginary scenario, once you passed the midpoint of the earth, you would then be fighting gravity. All the speed you picked up on the way down would slowly diminish as you rose up the other side.

So, your fall would send you past the center at roughly 18,000 MPH – this is ALMOST exactly enough force needed to get to the top again (or bottom, depending where you started of course). The trick comes in the “almost” part. It couldn’t really be the case that you’d pick up exactly as much speed as would be needed to reach the same spot on the other side. Some energy always finds a way to escape. Think of swinging on a swing. If you just push off once and then sit still, the swing doesn’t keep going back and forth forever. Gradually it slows down. It’s the same situation when you step into that hole. Down you'd go, and when you come out the other side, your feet will stop at slightly less than ground-level. If you miss your chance to grab onto something, you will fall though the entire planet again. Back at your starting place you rise slightly less than last time, and so on. So, you'd will wind up yo-yoing inside the tunnel, each time rising slightly less than the time before. Eventually you will stop moving altogether and be stuck in the middle–with a long climb home. However, If you ignored all of these factors or had a handy tree/someone to grab you when you popped out of the top/bottom of your hole scientists think it would take about 42 minutes to fall through the tunnel and pop out of the other side.

It matters where you live. You would ultimately reach the other side. For example if one lives in the United States, they would end up in the Indian Ocean, for it is the opposite of where one lives. 

Its led to migrationits led to death