ARCHIMEDES
PRINCIPLE


According to Archimedes principle:  
"When
a body is immersed in a liquid, it loses its weight or an upward thrust
acts upon it which is equal to the weight of an equal volume of the liquid
displaced."


PROOF
OF ARCHIMEDES PRINCIPLE

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Consider a cylinder of length 'L' and area of crosssection 'A' immersed in a liquid of density 'r.'  
Let the depth at point a = h_{1} the depth at point b = h_{2} Now, Pressure at point a and b is Pa = rgh_{1} , Pb = rgh_{2} We know that [Thrust = P . A ] Thrust at point a = rgh_{1}A Thrust at point b = rgh_{2}A Net thrust = rgh_{2}A  rgh_{1}A Net thrust = rgA(h_{2} h_{1}) [ But from figure h_{2} h_{1}= L ] There fore , Net thrust = rgAL Net thrust = rgV Net thrust = (rV)g Net thrust = mg Net thrust = W Net thrust = weight of liquid displaced. This shows that upward thrust on the cylinder is equal to the weight of liquid displaced. 
[ AL = V ] [rV = m ] [ W = mg ] 

RESULTS
OF ARCHIMEDES PRINCIPLE

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For
latest information , free computer courses and high impact notes visit :
www.citycollegiate.com With the help of Archimedes principle we conclude that: (1) A body will float over a liquid if displaces liquid whose weight is greater than the weight of body . (2) A body will sink in a liquid if it displaces liquid whose weight is less than the weight of body. 

Scientific Reason:  
Question
: A huge ship floats over water but a small nail sinks into water .
Explain why ? Answer : Floating of a huge ship or sinking of a nail is according to Archimedes principle. A huge ship displaces water whose weight is greater than the weight of ship & the upward thrust on the ship balances its weight. That's why ship floats over water surface. On the other hand nail displaces water whose weight is less than the weight of the nail. Due to this reason nail sinks into water. 

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