Do you know how Earth's Gravity really works?

hmmmm, it would excellerate to the center of the earth, swing up and down the shaft, pendulum-like, and then settle right at the center?

Or

It would be effected by the rotation of the earth and spiral against the wall of the shaft and then do the pendulum thing, but while spiraling?

And eventually hover in the center because it is essentially weightless?

It should decelerate before it reaches the center, as an increasing amount of mass is exerting a gravitational "above" (and on either side of) it.

It would behave very erratically, bouncing from side to side as it got near different kinds of ore or molten deposits, and then, as patiodog suggests, come to a shimmering, shaky 'rest' at the center. How does that sound?

True, the earth is not uniform density...

My short, and truer answer is "No, I don't know how the earth's gravity works." I await with baited breath.

The equation of motion for an object freely falling through a hole in the Earth can be shown to be that of an undamped harmonic oscillator. The object would free fall through the Earth, reach a maximum speed at the Earth's center, and slow to zero speed at the other side. Ignoring friction, the object would "yo-yo" from one side to the other indefinitely. The period of this motion is the same as that of a circular Earth orbit at treetop level: 84.5 minutes!

Yeah Yeah Yeah! Pendulum-like!

The fastest velocity obtainable by an object is described by straight line at an angle of 80.957 degrees with respect to the radius of the sphere.

I will refer to this maximum allowable velocity as c, short for "maximum allowable constant velocity." Imagine an object of the smallest possible dimensions moving with constant velocity c. I will call this a q object, for its quick behavior. As defined, the path of q would be at an angle of 80.957 with the radius of the sphere at every point along its trajectory. In three dimensions, q traces out a spiral around the center of the universe.

If velocity could reach 90 degrees, the path of the object would be nothing more than a circle describing the circumference of the sphere. Such an object would have to be in several places at once. Angles greater than 90 degrees imply that, while the universe expanded outward in the third dimension, the object describing this line somehow managed not to move along with the surface. Given our definition of matter, this simply isn't allowed. (~o)

The question was:

What would happen to the ball as it travels through the imaginary hole?

Here are some additional pieces of information that you should bear in mind when considering this question:

1. Air resistance
2. Temperature at the Earth's Core
3. The Earth's Precessional wobble

Okay, so the ball would actually melt before it made it to the other side. The answer, theoretically, is available all over the Web which is where I pulled this one (nobody asked but surely nobody believe that was in my head!)

(Not only that, it would create two lovely volcanos of catastrophic scale on either side of the Earth).

Lightwizard:
I guessed that someone would try to pull the answer to this question off the internet, so I tweaked the wording slightly and added a few physical values just to flesh the question out a bit.

Thank you for your honesty in declaring the originality of your answer. However, the true answer is not what you have stated, although other suggestions have come close.

You need to make full use of the three pieces of information that I posted earlier.

Here's my .02c worth of guess: As it 'gravitates' to the center of the earth, the rotation of the earth will pull at the ball like a yo-yo to the outer fringes (as somebody already surmised). No, make that .01c worth. c.i.

Not at all sure what you mean, Biblio. I knew that any object, regardless of its weight would eventually start moving back and forth within the Earth but didn't know how to express it using a forumla. I'm thinking that if you put the actual conditions at work on the ball that it's moot as it will melt as soon as it hits the magma. Not to mention the two volcanos if you're erasing all conditions.

This is why perpetual motion doesn't work (although they have a ball spinning in a magnetic field, I believe at Columbia University for over twenty years).

Light, The rotation of the earth is in "perpetual motion." c.i.

Until our sun novas.

Perpetual motion is something that was hoped to be a source of energy, not using any energy. Friction is its' chief enemy. We do use gravity and the spinning of the Earth as energy in shooting our explorer spacecraft out into space -- however, it assists a primary energy source.