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Selina Solutions Class 9 Physics Solutions for Exercise 5C in Chapter 5 - Chapter 5 Upthrust In Fluids Archimedes Principle And Floatation
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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}}
Answer:
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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