What would happen if a hole is dug in the centre of earth from north pole to south pole.?

First off, much of the interior of the earth is molten after you get about 30K down, so you couldn't really drill a hole through it. But for arguments sake, let's say you built a super-strong tube out of some nano-material and inserted it through the center of the Earth from pole to pole. Now you drop your stone.

The stone would fall towards the center of gravity, the center of the Earth. It would accelerate as it fell, so it would presumably fall past the center and head towards the South Pole. As it headed towards the South Pole, the gravitation pull would slow it down. Would it manage to to escape the Earth's gravity? No.

Consider that the stone being at the top of the North Pole represents "potential kinetic energy". You could have generated energy from its fall much like a dam creates energy from falling water. Instead, it fell freely towards the center of the Earth, and all its potential kinetic energy has been turned into velocity. That velocity can't be enough to go any further than it fell (that is, out of the South Pole) because where would the excess energy come from?

Now when the stone is at the center of the Earth, it has no potential kinetic energy. It can't fall anywhere, because every direction is up. All of its potential kinetic energy has been turned into velocity and so it should "fall up" the distance that it fell down. When it reaches the South Pole, it will have no velocity left, but it will have the same potential kinetic energy as when it started to fall. So you might expect it to fall from pole to pole indefinitely.

However, if the tube is full of air, we have a problem. Falling objects normally have a "terminal velocity", which is the speed at which the air resistance stops the object from accelerating further. The air pressure at the center of the Earth would be enormous (air would probably be a liquid at these pressures and temperatures), as it would be subject to the weight of the air both north and south of the hole pulled in towards the center. The increasing density of air would slow the object as it fell to where it had little momentum as it approached the center. It might overshoot somewhat, but friction would continue to slow it until it was drawn to the center of gravity.

Now if the tube contained a perfect vaccuum, the object should continue to fall from pole to pole indefinitely...except there's the problem that the stone would hit the sides of the hole due to the rotation of the Earth. See Foucault's Pendulum. This would slow it down, causing it again to settle at the center of the Earth.

There you have it. No need to drill through the center of the Earth now.

Well, you have to presume a lot here first. I'm assuming the lining of the hole is some sort of UBER-Plexiglas to hold back the magma and millions of pounds of pressure from the surrounding Earth.

That being the case, a stone drop from one side of the Earth would accelerate until it reached the center of the Earth (with calculus you could actually figure out the speed it would be going -- most likely terminal velocity). Then as it comes up the other side it would be decelerating. All other things being equal, the stone would pop out the other side, come to a stop at shoulder-level, and then fall back in. It would oscillate between the planet surfaces. If you made the hole directly along the tilt axis of the planet, it would do this forever -- otherwise I'd guess that the Coriolis Effect would make it hit the wall of the hole eventually.

Sounds like a cool ride if you ask me.

If we could have a shaft going right down to the center of the earth and back the other side, a stone falling into it would go though the center at great velocity, but passing though the center, would experience weightlessness, as it would be attracted by the earth mass distributed evenly all around. Its velocity would take it up the other side, slowing progressively down and it would pop up at zero velocity just as it emerges -- assuming there would not be any air resistance in the hole that is -- at the south pole. It would then fall back the other way, towards the north pole, bouncing back and forth between the two ends of the shaft.

No, it will keep oscillating in the hole.

As soon as you drop the stone, it will start accelerating towards the center of the earth and then at the center there will not be any center of gravity but because of momentum, it will pass the center and will slowly it will reach the south pole and then after a moment it will start backwards. This process will keep on going infinitely if there is no air resistance. But definitely it won't go into the space.

BTW, once you have dug the hole in the earth, let me know. I will be more than happy to throw the stone in it. :))

The stone would come up just to the surface at the south pole, stop briefly, just like any stone that you throw straight up stops briefly, and then fall back to the north pole. In the absence of any friction from the air it would swing back and forth from pole to pole forever. In the presence of air, friction would make it swing less and less so that over time it came to rest at the center of the Earth, where it would float, weightless, in the middle of the hole.

Since the theory that I believe in - expansion theory - states that gravity doesn't exist but instead the earth (and everything) is expanding outwards in all directions due to an imperceptible (its imperceptible because everything is expanding relativistically) subatomic expansion, the object would not actually fall but the earth would expand past it when you dropped it in the hole. It would come to a firm and abrupt stop when it reached the exact center of the earth.

The center of gravity is a mass - not a point. the core of 500 miles diameter would still be the center of the earth.

Might be interesting that the earth would whistle as it orbits. How big would the hole be? :)

No, it would collapse before it was thru the crust of the earth. Even still, you would strike magma half way thru, and thus the project would end.

why would u dig a hole anyway what is this about

you would be burned to death if you go near the core