State and prove Archimedes principle.

Explanation

Archimedes Principle, It states that when a body is partially or wholly immersed in a fluid, it experiences an upward thrust equal to the weight of the fluid displaced by it and its opthrust acts through the centre of gravity of the liquid displaced.
Proof: Consider a body of height "h" lying inside of destiny `rho` , at a depth bx below the freesurface of the liquid. area of cross section of the body is "a" . The forces on the sides of the body cancel out.
Pressure at trhe upper face of the body, `P_(1),=xrhog`.
Pressure of the lower face of the body,`P_(2)=(x+h)rhog`.
Thrust acting on the upper of the body is
`F_(1)=P_(1)a=xrhoga`
acting vertically downwards,
Thrust acting on the lower face of the body is
`F_(2)=P_(2)a=(x+h)rhoga`
The resultant force`(F_(2)-F_(1))` isacting on the body in the upward direction and is called upthrust (U).
`U=F_(2)-F_(1)=(x+h)rhoga-xrhoa=ahrhog`
But ah=V, Volume of the body=Volume of the liquid
`U=Vrhog=Mg`
Upthrust or buoyant force=Weight of liquid displaced .
This proves the Archimedes principle.