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Question

# A body is floating in water. 1/3rd of the body is inside the water and 2/3rd is in the air as shown in the figure. Find out the density of the body. ρw=Density of water ρb=Density of the body

A
ρb=ρw3
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B
ρb=ρw4
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C
ρb=2ρw3
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D
ρb=ρw2
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Solution

## The correct option is A ρb=ρw3It is given that 1/3rd of the body is submerged in the water. So, the volume of displaced water, Vw=V3 where V: Volume of the body Using Archimedes' principle, the weight of the body is equal to the weight of water displaced by the body. Wbody=Wdisplaced water ⟹ρbVg=ρwVwg ⟹ρbV=ρwV3 ⟹ρb=ρw3 Hence, the density of the body is 1/3rd of the density of the water in the container.

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