Three Liquids in U-shaped Container · CAP 2012 #10

Physics · fluid-mechanics

Problem

There are three different liquids, with densities ρ1\rho_1, ρ2\rho_2 and ρ3\rho_3, in a U-shaped container as shown in the picture. The lengths shown are H1=15H_1 = 15 cm and H2=10H_2 = 10 cm. Which of the following equations gives the correct relation between the densities of the fluids in the container? a) 3ρ3=2ρ1+ρ23\rho_3 = 2\rho_1 + \rho_2 b) ρ3=2ρ1+3ρ2\rho_3 = 2\rho_1 + 3\rho_2 c) 2ρ3=3ρ1+ρ22\rho_3 = 3\rho_1 + \rho_2 d) ρ3=3ρ1+2ρ2\rho_3 = 3\rho_1 + 2\rho_2 [Figure: U-shaped container with three liquids of densities ρ1\rho_1, ρ2\rho_2, and ρ3\rho_3, with heights H1H_1 and H2H_2 marked]

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