Why does the centre of buoyancy act on the centre of the submerged part of a solid floating in a fluid.

1.One explanation that I came across previously was based on the fact that the fluid displaced by the solid was in vertical equilibrium before solid was immersed. so there must be a force equal to the weight of the volume displaced acting and that too at a point that coincides with the centre of mass of the fluid..

2.My doubt is that is there a mathematical proof of the same?


Ignoring the dynamics effects of the shape, you can approximate distributed masses as a point mass located at a "centre of mass".

In the case of simple analysis of a buoyant object, we often only care about it's equilibrium height. Therefore we can approximate the force as a single force acting purely on the centre of mass, compared to a distributed force acting on a distributed mass. The wikipedia article should explain the mathematics in depth.

If we were concerned about things like rotation and force distribution over the surface of the object, we would need to look at the actual shape.

It's also worth noting that for more complex shapes/vessels, the centre of buoyancy is not the same as centre of mass. This has implications for stability of a buoyant object. See here for a diagram somewhat showing this.


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