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State and prove Archimedes principle. |
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Answer» Solution :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. 
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