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Archmedes' Principle says that If a body is totally or partially immersed in a fluid, it experiences an upthrust equal to the weight of fluid displaced.
By experiment, It is found that
Apparent loss in Weight = Upthrust =Weight of water displaced
In the Bouyant force, We know that if an object floats in water
Weight of liquid displaced by the submerged part of the object = Weight of object
Because If an object floats, then its apparent weight is zero. (If its apparent weight is more than zero, it sinks). A floating object appears to have lost all of its weight.
So, Apparent loss in weight = Actual weight.
Mathematical Proof
A solid cylinder of height 'h' and area of cross-section 'A' , to be completely immersed in a fluid of constant density p.
FB = h₂pgA – h₁pgA
= A(h₂ – h₁)pg = Vpg.
V is the volume of cylinder submerged in liquid.
Upthrust = weight of the liquid displace.
The bodies of average density greater than that of liquid, sink in it.
The bodies of average density equal to or smaller than that of liquid, float in it.
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