Question: If you dig a hole right through the earth, and drop a ball through it, what will happen to it? ( I got asked this question in my oxford interview practice...lol. So just wanna see what you think?)
If there was no air resistance (or any other effects from variation of the density of the Earth’s core), the ball would leave your hands, accelerating towards the centre of the earth – and will keep accelerating until it reachest it’s maximum velocity as it passes the centre of the Earth. Once it passes that point, it would start decellerating – and would reach a stop at the other side of the earth – it would then accelerate back towards the centre of the Earth, and so on and so forth – simple harmonic motion! Of course there are other factors in reality which would mean this wouldn’t be viable – like drilling a hole through the Earth!
I think the answer is this (though maybe look it up if you think you’ll really get asked that as an interview question, I wouldn’t want to feel responsible!!):
The ball will be travelling through air so at some point when you drop it will reach terminal velocity. As it reaches the centre the gravitational force on it is smaller and so after it passes the centre it will oscillate about the centre and eventually come to rest at the centre of gravity. (If there were no air I would expect it would go through & out the other side to the opposite of where you dropped it and then oscillate the full way back and forth through the Earth without coming to rest.)
The easier answer is that it will melt as it approaches the centre and get stuck to the sides of the hole you’ve drilled :-p
The ball will initially accelerate at 9.81 m/s^2 towards the center of the Earth due to gravity. But as it picks up velocity, its acceleration will decrease because more and more mass will be above the ball and less and less below it. The increasing mass will cause an opposite effect to gravity and that will offset the decreasing gravity pull down.
The net gravity force will go to zero as the ball approaches the center of the Earth.
Now we have to imagine that the Earth is cool in the middle because otherwise the ball will just vaporise with the temperature and the pressure. When the ball reaches the center of our imaginary cool Earth, it will have reached about 28000 km/h, and the mass above it would equal the mass below it. This means the force of gravity will be pulling it equally from all around, so the gravity forces cancel out and there is no net force acting on the ball when it’s dead center. Acceleration at this point will be exactly zero.
But the ball’s momentum p = mV will be at its maximum. With no forces acting on it to stop the ball, it carries on right through the center and starts its rise to the other side of the Earth. As it ascends, it’s acceleration, which is now a deceleration, increases at the same rate it decreased when heading toward the center.
In other words, the ball will follow a mirror image of the trajectory it travelled when heading inbound to the center. Instead of increasing velocity, the initial 28000 km/h velocity decreases at increasing deceleration as more and more of Earth’s mass is behind it and less and less is above it. Finally, when it reaches the surface on the other side, it will have reached zero velocity with an acceleration of 9.81 m/s^2 back toward the center of the Earth, but from the other side this time.
And if no one is there to catch that ball as it pops up on the other side, it will fall back down into the hole and start the journey all over again!!