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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=2ρw3
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C
ρb=ρw4
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D
ρb=ρw2
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Solution

The correct option is A ρb=ρw3
It 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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