State and prove Archimedes principle.

Explanation

Archimedes Principle : It states that when a body is partially and wholly immersed in a fluid, it experiences and upward thrust equal to the weight of the fluid displaced by it and it.s up trust act through the centre of gravity of the liquid displaced.
Proof: consider a body of height .h. lying inside a liquid of density `rho`, at a depth x below the free surface of the liquid. Area of cross section of the body is .a.. The forces on the side of the body cancel out.
pressure at the upper face of the body, `P_1 = x rho g`
Pressure at the lower face of the body, `P_2 = (x + h) rho g`
Thrust acting on the upper face of the body is, `F_1 = P_1 a = (x + h) rho g a`
Acting vertically downwards,
The resultant force `(F_2 - F_1)` is acting on the body in the upward direction and is called upthrust (U).
`U = F_2 - F_1 = (x + h) rho g a - x rho g a = a h rho g`
But ab = V , volume of the body = Volume of liquid
`U = V rho g = Mg`
i.e., Upthrust or buoyant force = weight of liquid displaced . The proves the Archimedes principle.