Neutral buoyancy and free fall

Question

Is an object that is neutral buoyant the equivalent of the same object in the microgravity (free fall) of the International Space Station?

If a pingpong ball floating on top of still water in a basin is it identical (not including the surface tension of the water) as a pingpong ball experiencing free fall in the International Space Station (not counting the difference in the distance to the center of the earth)?

Would the pingpong balls behave in the same way to the attempt to set them in motion on the horizontal plane or bring them to a complete rest with respect to the rooms in which they are in?

Edit: I see parts of my question are poorly worded to get the answer I'm looking for. The first question is what I'm curious about. Is neutral buoyancy the equivalent to free fall in orbit?

Answer 1

Is an object that is neutral buoyant the equivalent of the same object in the microgravity (free fall) of the International Space Station?

In some ways they are very similar, in other ways, not so much. In either case, the net weight is (approximately) $0$. This is the major similarity.

Some differences would depend on the medium that you are buoyant in. For example, if you were neutrally buoyant in air (not sure how exactly you would achieve that), it's different than neutral buoyancy in water.

Neutral buoyancy in air would be practically the same as free fall, as far as I know. Neutral buoyancy in water would be quite different, because water has a lot more drag, so your movements would be stopped a lot sooner. There's more resistance to motion. Being neutrally buoyant in water would also cause a greater surface pressure on the submerged person/object.

Now, there seems to be a big misconception in your question I would like to address:

If a pingpong ball floating on top of still water in a basin is it identical (not including the surface tension of the water) as a pingpong ball experiencing free fall in the International Space Station (not counting the difference in the distance to the center of the earth)?

A ping pong ball floating on top of still water is not an example of neutral buoyancy. It's an example of positive buoyancy. Neutral buoyancy is when the buoyant force equals the weight on a fully submerged object. That would allow you to put it at any elevation as long as it's fully submerged, and it would stay there without moving up or down. A ping pong ball will have an upwards force when fully submerged, and will be forced out of the water. It is not neutrally buoyant.

For an object to be neutrally buoyant, it needs to have the same average density as the fluid it is displacing. This can be shown from Archimedes principle, where buoyant force is equal to the weight of the fluid displaced. When the object is the same density as the fluid, the volume it displaces will always weigh the same amount as the object, so it becomes functionally weightless when submerged in that fluid.

Answer 2

One obvious difference is that the neutral buoyancy state of the ping pong ball on water is broken if it is moved vertically. If it is lifted and released it will fall back to the water surface; if it it pushed down and released it will rise back to the water surface. Whereas the ping pong ball in the ISS can be moved in any direction.

Another difference is that even if we restrict ourselves to movement in the horizontal plane, the ping pong ball on water will experience a significant amount of drag if it is moved. For the ping pong ball in the ISS there will be some drag (due to air resistance) but it will be much less.

I would say there are more differences than similarities between the two scenarios.