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A body of volume V and density ρS floats with volume v inside a liquid of density ρL. Show that

\frac{v}{v}=\frac{\rho_{S}}{\rho_{L}} Looking to do well in your science exam ? Learn from an expert tutor. Book a free class!

To prove

\frac{v}{v}=\frac{\rho_{S}}{\rho_{L}} V to be the volume of the body having density ρS ‘v’ to be the volume of the body when immersed in a liquid having density ρL

The weight of the body can be given by:

W = volume of the body x density of the body x g

= V ρS g

Upthrust or the weight of the liquid displaced by the body is given by:

FB = volume of the liquid displaced x density of the body x g

= v ρL g

We know that for floatation, FB = W

 V ρS g = v ρL g

\frac{v}{v}=\frac{\rho_{S}}{\rho_{L}} Hence proved.

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