Question

A body of volume V and density ρs, floats with volume v inside a liquid of density ρL. Show that v/V = ρsL

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Answer

Volume of body = V

The volume of body submerged in liquid = v

Density of body = ρs

Density of liquid = ρL

Let weight of the body be W. W = volume of the body x density of the body x g = V ρs g

The weight of the liquid displaced by the body will be equal to the upthrust. Let it be FB.

FB = volume of the liquid displaced × density of the liquid × g = v ρL g

From the principle of floatation,

W = FB

⇒ V ρs g = v ρL g

{v\over V} = {ρ_s\over ρ_L}

Hence proved.

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