If you were drill from one side of the earth to the other?
If you were drill a hole straight down from where your standing to the opposite side of the globe would you come out upside down? Never mind the whole “err you wouldnt make it through the core or we dont have a drill that would let us do that” its a simply theoretical question.
As you go down deeper the gravitational force on you will decrease.
When you reach the center the force will become zero.
Case 1(Not a free fall , but rather a crawl descent into the hole):
When you go beyond the center, say with your head first you will start experiencing a force that pulling your legs towards the core. You will feel like wanting to rest your feet somewhere, as if you are falling to the center.
Now its up to you. If you have some mechanism to continue your travel further from the center by travelling against the g force, YES, you will come out head first from the other end.
Case 2(Free fall through the hole):
If say there was a free passage through the center of the earth and you were just dropped head long. You would go all the way to the other way again with your head first and then continue to fall back to where you started, in a two and fro motion , which could continue forever if some kind of friction or viscosity of air does’nt impede your motion ( if something did impede your movement you would finally come to rest at the core).
So YES if you were dropped in the hole that you dug through the center, you WOULD come out the opposite of what you entered the hole as(head/feet first).
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