why does an object float in the centre of water?

It is pretty clear from archimedes that how an object behaves in terms of floating and sinking when submerged in a liquid is cleary a matter of density of both the object and the liquid. SO consider an infinitely big aquarium , in front of which a man is standing ; the man somehow throws balls into the middle of the aquarium with a finite horizontal velocity. These balls have a density that is equal to that of the liquid in the aquarium . These balls will stop after some time , but after the balls have stopped will they continue to rise vertically in the aquarium ? some time later ............... the same man throws balls vertically into a river . this time also the balls have same velocity as that of water. When the balls stop will rise up or remain at that position where they have stopped ?

the Archimedes principle tells me that they will not rise but remain at that spot. I just need a reassurance !

Also i need to clarify one more fact ; if thrown vertically in a big body of water, is it possible for a object with a greater density than that of water to stop midway in the river due to greater density at that point or does this type of object have a enough water level above it which will cancel out the effects of the greater density below ?

If I understood your question correctly, then assuming still water, its density minutely increases with the depth. The object floating at any level, has same density as that of water at that level. This is ignoring internal currents etc. of the water.

In rare cases, the object at a depth may get compressed due to water pressure at that depth and attain a density that is greater than that of water at that level and may sink further. Depends upon what gets compressed more due to water pressure - water itself, or, the object. But eventually it will float at a level where its density matches with that of water, assuming it does not cross the level where its compression rate exceeds that of water.

• do you have any mathametical equation which determines whether what gets compressed more due to water pressure - water itself, or, the object. Feb 18, 2016 at 6:01
• No, sorry, that would depend upon the nature of the object.
– kpv
Feb 18, 2016 at 6:02
• but nature of an object can itself be expressed by an equation , however i think depth does not increase the density of a submered object because if depth increases downward pressure on an object an equal upward pressure from below will be exerted on the object , because there will be a more ense liquid below the object Feb 18, 2016 at 6:37
• I do not have any equations. Everything in depth experiences a crushing pressure from all directions. That is what I mean by compression.
– kpv
Feb 18, 2016 at 7:11
• but we have nothing to do with compressions . Fine i am doing an edit , so that my question is clear .. Feb 18, 2016 at 7:19