What would a actually happen I suppose would depend on the mass and shape of whatever object is dropped. Suppose it were a perfect sphere weighing ten pounds, cropped into a hole twice the diameter of the sphere?
My hunch is that it would stop at the center (taking only gravity into account and not the forces caused by heat).
The ball would achieve its maximum velocity in a few seconds (like a skydiver), then slow down a bit because the atmospheric pressure would increase in the descent, then because the Earth isn’t uniformly dense, would start rolling down the side of the tunnel.
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