Question
State and prove Archimedes principle.
Solution
Archimedes principle: When a body is immersed partially or wholly in a liquid, its weight appears to be reduced and loss of weight is equal to the weight of liquid displaced by the body.
Proof: Consider a body of height h and area of cross-section A placed in liquid of density σ at a depth x below the free surface.
Let ρ be density of the body.
where, P0 is atmospheric pressure.
Pressure at the lower face of the body is,
Therefore downward thrust on upper face of the body is,
and upward thrust on lower face of body is,
Since P2 > P1 therefore F2 > F1
Body will experience the net force F2 - F1 in upward direction known as upward thrust.
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where, V is volume of body
= Weight of liquid displaced by body.
Now, the body experiences two forces: weight of the body itself and upward thrust.
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i.e. Apparent weight is less than the actual weight by amount equal to weight of liquid displaced by body.
