Question

You come across an open container filled with two liquids. Since the two liquids have different densities, there is a distinct separation between them. Water, which has a density of 1.00×1031.00×103, fills the lower portion of the container to a depth of 0.212 m.What is the density of the second liquid if the total depth of the liquid in the container is 0.300 m?

A. 1.25×103
B. 1.50×103
C. 1.75×103
D. 2.00×103

Answer 1

The density of the second liquid can be found by using the difference in depths and the known density of water to calculate its mass, then equating that to the mass of the second liquid assuming equal volumes for a fixed container area.

Step-by-step explanation:

The density of the second liquid in the container can be calculated using the principle that the total mass of the liquids is equal to the sum of the masses of the individual layers, given the total depth is known. Since water fills the lower portion to a depth of 0.212 m, and has a known density of 1.00×103 kg/m³, we can determine the density of the second layer by allowing for the total depth of the liquids combined to be 0.300 m. The depth of the second liquid would then be 0.300 m - 0.212 m = 0.088 m. Assuming that the container has a uniform cross-sectional area, A, the mass of the water is mwater = Densitywater × Volumewater, and the mass of the second liquid is mliquid = Densityliquid × (A×0.088 m). As the total mass and volume are the same for both layers, by equating the two and solving for Densityliquid, we can calculate the second liquid’s density.