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Question

A body is floating in a beaker filled with water. 1/3rd of the body is inside the water and 2/3rd is in the air as shown in the figure. What will be the density of the body.
ρw=Density of water
ρb=Density of the body [3 marks]


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Solution

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. [1 mark]

Wb=Ww

ρbVg=ρwVwg

ρbV=ρwV3

ρb=ρw3

Hence, the density of the body is 1/3rd of the density of the water in the container. [2 marks]

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