Two objects of different shapes, sizes, and materials, are floating in water (density 1000 kg/m3). Object A floats with 60% of its volume submerged, while object B floats with 50% of its volume submerged. What can be concluded about the densities ρA and ρB of the two objects?
Question
Two objects of different shapes, sizes, and materials, are floating in water (density 1000 kg/m3). Object A floats with 60% of its volume submerged, while object B floats with 50% of its volume submerged. What can be concluded about the densities ρA and ρB of the two objects?
Solution
The density of an object floating in a fluid is determined by the percentage of the object that is submerged. This is based on Archimedes' principle, which states that the buoyant force (the force that makes the object float) is equal to the weight of the fluid displaced by the object.
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Calculate the density of object A: Since object A has 60% of its volume submerged, it means that it displaces 60% of its own volume of water. The density of object A (ρA) is therefore 60% of the density of water. Since the density of water is 1000 kg/m3, ρA = 0.60 * 1000 kg/m3 = 600 kg/m3.
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Calculate the density of object B: Similarly, since object B has 50% of its volume submerged, it displaces 50% of its own volume of water. The density of object B (ρB) is therefore 50% of the density of water. So, ρB = 0.50 * 1000 kg/m3 = 500 kg/m3.
Conclusion: Therefore, we can conclude that the density of object A (ρA = 600 kg/m3) is greater than the density of object B (ρB = 500 kg/m3).
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