Question

# A body floats in water with its one-third volume above the surface. The same body floats in a liquid with one-third volume immersed. The density of the liquid is:

A
9 times more than that of water
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B
2 times more than that of water
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C
3 times more than that of water
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D
1.5 times more than that of water
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Solution

## The correct option is B 2 times more than that of waterBody floats in water with its one-third volume above the surface, so according to law of floatation, we have weight of the body = upthrust in water⇒W=(2V3)ρwg .....(I) Since two-third volume is under the water. And applying the same for the liquid, we have ⇒W=(V3)ρlg .....(II)from (I) and (I), we have (2V3)ρwg=(V3)ρlg⇒ρl=2ρw

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