How do you derived formula of buoyant force?

Answer 1

well it's easy..:D

we consider a cylindrical portion of a liquid and find that on an average the object(water itself) remains stationary.

This gives us an idea that the upward force(buoyant force) equals the gravitational force.

Therefore the buoyant force in this case is the "mg" itself but in fluids we talk in terms of the volume and density so it is V(rho)g.

Plus this buoyant force in any case is independent of the object coz' it is fundamentally rooted to the Brownian motion and striking of the particles on the object which leads to the upward force.

So it only depends on the volume of the object.

And the buoyant force is defined as Volume *density of liquid*g.

Answer 2

The formula for buoyant force is derived from Archimedes' principle, which states that the buoyant force acting on an object in a fluid is equal to the weight of the fluid displaced by the object. Mathematically, the buoyant force (Fb) is given by Fb = ρ × V × g, where ρ is the density of the fluid, V is the volume of fluid displaced by the object, and g is the acceleration due to gravity.