Gravity's tall box with a ball inside - scenario Let's imagine we put a ball inside a box such that it doesn't touch its walls, and suddenly drop the box. Because the two objects fall at the same rate of acceleration, the ball will stay at the same distance from the walls of the box while on free fall. Correct?
Now, let's imagine the same scenario but with a really long box; one that extends from a few hundred meters off the surface of the Earth all the way to outer space where the force of gravity is much weaker. Let's imagine we put the ball inside the box, near the wall of the outer space side.
What would happen when we drop the box? The Earth surface side of the box will tend to fall at a much faster acceleration than the outer space side of the box. Will the outer space side of the box be pulled down by the Earth surface side causing the outer space side to fall faster than it normally would? Then, does that mean the ball would collide with the outer space side's wall?
 A: Yes, in the situation you describe the ball will collide with the outer wall of the box.
This is an example of a tidal force. Suppose you are floating right in the centre of the box (specifically at its centre of mass), then you and the box will fall at the same speed so you'll appear to be hovering weightless at the centre of the box. Suppose you now release the ball slightly nearer the Earth than you are. Because gravity is slightly stronger at the ball's position it will start moving away from you towards the Earth and will eventually hit the side of the box nearest the Earth. Conversely, if you release the ball slightly farther from the Earth than you are the ball will start moving away from you in the direction away from the Earth and it will eventually hit the far side of the box.
On the other hand, if you hold the ball out sideways and release it at exactly the same distance from the Earth as you are, but displaced sideways, then when you release the ball it will start moving towards you.

As you and the balls fall towards the Earth the red balls will move away from you and the green balls will move towards you.
You might have heard that anything falling into a black hole gets spaghettified, i.e. stretched out into a long string. This is a result of the same tidal forces I've described above - just in a more extreme form.
