So therefore, the upward force is equal to gamma times V, but

gamma times V is just the weight of the fluid which is displaced by the body.

Therefore, the final conclusion is that the buoyancy force is equal

to the weight of the fluid, which is displaced by the body which is of course,

Archimedes principle, and it acts through the Centroid of the body.

If we have a floating object, then the buoyancy force

is equal to the weight of the volume which is displaced.

In other words, it's the weight of the volume which is displaced by the submerged

portion of the volume, and it acts through the Centroid of that displaced volume.

Not the Centroid of the volume of the whole, but

the Centroid of the volume which is displaced.

Now, the next question I want to look at briefly is the stability of an object.

If the object is of uniform density, the Centroid of the volume,

and the center of gravity are in the same place.

The Centroid is a purely geometrical thing,

it only depends on the shape of the object.

So, if it's of uniform density, the Centroid and

the center of gravity are at the same place.