|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
|Consider a cylinder of length 'L' and area of cross-section 'A' immersed in a liquid of density 'r.'|
the depth at point a = h1
the depth at point b = h2
Pressure at point a and b is
Pa = rgh1 , Pb = rgh2
We know that
[Thrust = P . A ]
Thrust at point a = rgh1A
Thrust at point b = rgh2A
Net thrust = rgh2A - rgh1A
Net thrust = rgA(h2- h1)
[ But from figure h2- h1= 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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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.
: 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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