if you dig a hole through the earth, from one hemisphere to the other, and drop a tennis ball into it, would it get stuck at the center, since thats where gravity's at, or would it pop up out the other side??

Depending on which hemisphere it is, like western to eastern, It would most likely get stuck at the center. You would also have to put more things into thought like acceleration, velocity, and speed.

BUT since the question asked "would it pop out the other side?", I'm assuming it's talking about northern to southern hemisphere. so in that case it would pop out the other side since gravity makes things go downwards.

We drop a tennis ball into the hole. The stone is pulled down towards the center of the earth. It falls all the way to the middle of the earth once it reaches the middle, theres no more pull of gravity. ... It would go up a ways, then (due to the pull of gravity) fall back in the other direction, back towards the center

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