Question

A block of material has a density rho_(1) and floats three-fourth submerged in a liquid of unknown density. Show tht the density rho_(2) of the unknown liquid is given by rho_(2)=(4)/(3)rho_(1).

Answer 1

To prove : The density ρ₂ of the unknown liquid is given by ρ₂ = (4/3) ρ₁

Proof :

• Let us consider that,

       m = mass

       g = acceleration due to gravity

       V = volume

       σ = density

• As per the question, a block of material having density ρ₁ floats 3/4th submerged in a liquid of unknown density.

• Therefore, weight = upthrust

                               m g = V σ g

                           V ρ₁ g = ( 3 / 4 V ) ρ₂ g

                                 ρ₂ = 4 / 3 ρ₁

• Hence, proved.