Physics
A body of volume V and density ρs, floats with volume v inside a liquid of density ρL. Show that = .
Fluids Upthrust
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Answer
Given,
Volume of body = V
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
Weight of liquid displaced by the body will be equal to upthrust. Let it be FB.
FB = volume of the liquid displaced x density of the liquid x g = v ρL g
From principle of floatation,
W = FB
⇒ V ρs g = v ρL g
⇒ =
Hence proved.
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