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What fraction of ice is submerged when it floats in freshwater, given the density of water at 0°C is very close to 1000 kg/m³?

A. 0.9
B. 0.8
C. 0.7
D. 0.6

User Cagcowboy
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1 Answer

2 votes

Final answer:

Approximately 91.7% of the ice is submerged in freshwater based on the densities of ice and freshwater and Archimedes' Principle, which makes Option A (0.9) the closest correct answer.

Step-by-step explanation:

To determine what fraction of ice is submerged when it floats in freshwater, we use Archimedes' Principle, which states that the buoyant force on an object in a fluid is equal to the weight of the fluid displaced by the object. The density of ice is known to be about 917 kg/m³, and the density of freshwater at 0°C is approximately 1000 kg/m³. To float, the weight of the displaced water must equal the weight of the ice. Thus, the volume of water displaced will have a mass of 917 kg, if the volume of ice is 1 m³ (since density is mass/volume, and we're considering the unit volume of ice). If V is the fraction of the ice submerged, then V × (density of water) = density of ice, which gives us V × 1000 kg/m³ = 917 kg/m³. Therefore, V = 917 kg/m³ / 1000 kg/m³ = 0.917. This means 91.7% of the ice is submerged when it floats in freshwater, and looking at our options, we can see that Option A (0.9) is the nearest correct answer to this calculation.

User Cherron
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