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7.6 ARCHIMEDES PRINCIPLE
An air filled balloon immediately shoots up to the
surface when released under water. The same would
happen if a piece of wood is released under water. We
might have noticed that a mug filled with water feels light
under water but feels heavy as soon as we take it out of
water.
More than two thousand years ago, the Greek
scientist, Archimedes noticed that there is an upward
force which acts on an object kept inside a liquid. As a
result an apparent loss of weight is observed in the
object. This upward force acting on the object is called
the upthrust of the liquid. Archimedes principle states
that:
When an object is totally or partially immersed in a
liquid, an upthrust acts on it equal to the weight of
the liquid it displaces.
Consider a solid cylinder of cross-sectional area
A and height h immersed in a liquid as shown in figure
7.18. Let h and h be the depths of the top and bottom 1 2
faces of the cylinder respectively from the surface of the
liquid.
Then
If P1 2
and P are the liquid pressures at depths h1
and h respectively and  is its density, then according to 2
equation (7.3)
Let the force is exerted at the cylinder top by the
liquid due to pressure P and the force F is exerted

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