Lets say the Earth is hollow and you are in the center of it (Same mass except all of it is on the outside like a beach ball) If you move slightly to one side now your distance is closer to that side therefore a stronger gravitational force however at the same time you have more mass now on the other side. At what rate would you fall? Which direction?
Also, is there a scenario where depending on the radius of the sphere you would fall the other direction or towards the empty center?
If the mass/charge is symmetrically distributed on your sphere, there is no force acting on you, anywhere within the sphere. This is because every force originating from some part of the sphere will be canceled by another part.
Like you said, if you move towards on side, the gravitational pull of that side will become stronger, but then there will also be "more" mass that is pulling you in the other direction. These two components cancel each other exactly.
The answer is that inside a spherically symmetric shell of matter (your hollow earth or massive beach ball) there is no gravitational force anywhere - you will not "fall" in any direction, whether you are at the centre or not, regardless of the radius of the sphere.
This is a classic result of both Newtonian Gravity, and Einstein's General Theory of Relativity. In both cases it is called the [ ] Shell Theorem. Although, except at the centre, you are closer to one side than the other you can imagine that there is "more" farther away than there is closer, and because of the nature of the 1/r^2 law of Newtonian gravity everything cancels out. It is of course more complicated in General Relativity.
For a simple introduction, see the Wikipedia article on the Shell Theorem
You may also be interested to know that according to General Relativity time passes more slowly inside a hollow massive sphere than it does outside.
Whilst there is no gravitational force inside the sphere, and therefore no gravitational field, there is a non-zero gravitational potential - it just happens to be the same everywhere. Since the force of gravity depends on potential difference (just like voltage in the electrostatic case), if the potential is constant there can be no force. However, the potential does effect the passage of time in General Relativity, and since it is not zero inside the sphere time passes differently. Inside an "ordinary" matter sphere time passes more slowly.
