what happens to something thrown from the middle of earth?

To answer we have to accept your teacher's assumptions eg no temperature problems, earth is a uniform sphere, no air resistance, no external effects due to the sun,moon or planets, your own mass can be ignored for the purpose of the experiment etc.

If you release exactly at the centre the ball will remain motionless.

If you release from 1 m above the ball will accelerate down (not at 9.81 m per s per s), stop, accelerate back up again and oscillate forever.

Consider the effects of the other assumptions.

John

If the stone is small and is not being melt when getting closed to the core, the motion is like when a pendulum of an old clock is released. When it is passing the lowest position, where the acceleration is zero but it moves at a constant velocity to hit the core. It is because of the decrease of gravitational attraction when is related to the effective mass of the earth to the stone.

If the hole passed through the earth, the stone can go to the other side.
i.e. drop a stone from the North pole and come out from the South Pole. Alternatively, dropped from US and comes out from China.
If nobody take it from China, it will fall back to US again.
The oscillation will continue with decrease in height upon time because of air friction lost.

In other words, it undergoes simple harmonic motion.
Your teacher will tell you more about it later.

The force of gravity decreases as one goes towards the centre of the earth and it becomes zero at the centre. So, the ball will accelerate downward (with decreasing magnitude) until it reaches the middle of the earth and then it will start to decelerate(with increasing magnitude) and by the time it reaches the other side of the earth it's velocity will be zero.

this is an exciting question. Lewis Carroll (Alice in Wonderland, etc.) thought approximately this quite plenty. the middle of the earth is quite warm. hundreds of ranges. regardless of you dropped in could probably soften. Assuming it could desire to not soften, it could keep accelerating (do you comprehend the cost of acceleration for the Earth? look it up) till it reached the middle, then it could proceed as though thrown in the air. it could probably in basic terms omit the exterior on the different edge of the planet, then start up falling returned in direction of us. each and every time it did this, it could fall much less & much less till it ended up in the middle, not shifting. this could take a very long term! a large question is, how long could it take to get to the different edge of the Earth? i'm going to wager you are able to discern this out on your guy or woman!

If the hole is a perfect vacuum and the object never touches the sides of the hole, it will oscillate forever between one side of Earth and the other.

If there is air in the hole, or anything else to deviate the system from a vacuum-perfect solution, the object will eventually come to rest. Not necessarily at the center, if there is some ledge it can land on.

Of course, one could not actually do this since Earth's mantle has a consistency of heavy goo or sludge, and a hole would not sustain through it, and then the outer core is liquid, and the inner core is moving at a different speed than the rest of the planet, and any hole dug sufficiently deep would be likely to turn into a volcano.

the object will accelerate wid 9.8m/s^2 and goes on decreasing untill it reaches the centre where there will be no gravity. as the body was moving previously it will not stop at the centre but its acceleration will be uniform for a while and then it will start accelerating untill it comes from the othr side of earth.

Your physics teacher might be pointing you towards Shell therom (see the link).

From Wikipedia

Isaac Newton used shell theorem to show that:

1. A spherically symmetric body affects external objects gravitationally as though all of its mass were concentrated at a point at its center.
2. If the body is a spherically symmetric shell (i.e. a hollow ball), no gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell.
3. Inside a solid sphere of constant density the gravitational force varies linearly with distance from the center, becoming zero at the center of mass.

The question is: Which applies to your problem, 1, 2 or 3?

This might be prepping you toward Gauss' flux theorem for gravity if you are studying vector calculus. I was watching a lecture on iTunesU (Lenoard Susskind) and a similar question was posed (drop a mass into a well that goes to the center of the earth). I think the answer as that it oscillates according to Hookes Law.

Good Luck

i think it would hover in the centre of earth . during the fall it will gradually slow down i guess and finally comes to a stop at the center.

If we neglect the Earth's temperature at the core then the ball will continue to fall down at g (9.8 m/s/s) until it reach the center which then the ball would be stuck there... since gravity will be pulled from all directions.

You will get to the center and not go anywhere after that as you are in the center of gravity.