# Changes in force required to push buoyant object under liquid/water

If we have buoyant object, for the sake of this question, let's say it is a cylinder, 1" in diameter and 4" long. This cylinder is completely sealed so not liquid can enter and we have it arranged vertically. Also, let's assume it has little weight to it (meaning it is hollow and empty and the only weight to it is the material it is made of, like a float).

With that visual setup, the question is, imagine I have a deep tub of water. As I start to submerge this float but pushing down on the top of it, I know it is going to take more force pushing down on top, to submerge it the deeper I go. So, if only the first 1" is submerged, that would take less force on the top than if I submerged to 2". That is correct, right?

Now, to follow up on that, once the item is completely submerged (in this case, all four inches of it are under water) does the force required max out and become consistent? In other words, If I am holding it 8 inches underwater versus 16 inches under water, would that take the same amount of force now that I am fully submerged?

Thanks!

• Archimedes' principle : Archimedes' principle indicates that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and it acts in the upward direction at the centre of mass of the displaced fluid. See also my answer here (user82794) : physics.stackexchange.com/questions/196840/… Dec 14 '16 at 20:44

$F_B = p_w V g$
Where $F_B$ is the buoyant force, $p_w$ is the density of water (1g/ml), $V$ is volume of the water displaced, and $g$ is gravity. The key here is $V$.