That is a really interesting question. The exact acceleration depends on the density profile of the earth. But you are correct there is no gravitational pull in the center of the earth, it cancels out.
This is actually true for every spherically symmetric shell - gravity cancels out everywhere inside the shell. Something probably every physics undergrad had to prove as homework. See https://en.wikipedia.org/wiki/Shell_theorem for more information.
So when calculating gravity you only have to take into account the part of the earth below you, everything above you cancels out (yes the earth is not a perfect sphere but this is a pretty good approximation).
The end result for a large hole through the earth is oscillating around the center and slowing down until you are stuck in the middle. Oh and you would also be melting, it’s still ~6000° C down there.
That is a really interesting question. The exact acceleration depends on the density profile of the earth. But you are correct there is no gravitational pull in the center of the earth, it cancels out.
This is actually true for every spherically symmetric shell - gravity cancels out everywhere inside the shell. Something probably every physics undergrad had to prove as homework. See https://en.wikipedia.org/wiki/Shell_theorem for more information.
So when calculating gravity you only have to take into account the part of the earth below you, everything above you cancels out (yes the earth is not a perfect sphere but this is a pretty good approximation).
The end result for a large hole through the earth is oscillating around the center and slowing down until you are stuck in the middle. Oh and you would also be melting, it’s still ~6000° C down there.