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Please go through the 3 statements provided in the picture first and read below.

I understand all three statements except the last statement which states "A floating body displaces an amount of fluid equal to its own weight." If so is assumed then, we come to conclude the same result as statement two in the picture attached.How can we reach the conclusion of statement three(density of object is smaller than that of liquid) of the picture assuming "A floating body displaces an amount of fluid equal to its own weight." Also this always leads to weight of body(W) = Upthrust experienced by it (U), doesn't it?

Picture from my book.

Further reference at http://www.tutorvista.com/content/physics/physics-i/fluids-pressure/floating-bodies.php

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the body wants to be in equilibrium. It means net force on it should be 0.

So if body displaces some more liquid then that would further increase the buoyont force and hence more than the weight which would cause inequilibrium.

A familiar example makes it more clear ,

an empty mug floats on water with negligible volume inside the water in a bucket. But once you apply force in such way that it's empty face is upward and you pushing it down vertically in water ! What happens when you remove your hand ? It jumps out suddenly !

well that would give you the idea for the third statement.

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