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A metal sample weighs 210 g in air, 180 g in water, and 120 g in an unknown liquid. Which statement is correct?
- the density of the metal is 3 g/cm³
- the density of the metal is 7 g/cm³
- the density of the metal is 4 times the density of the unknown liquid
- the metal will float in water
Correct answer: the density of the metal is 7 g/cm³
Solution
Loss of weight in water = 210 - 180 = 30 g (this equals the mass of displaced water, so volume = 30 cm³). Density of metal = 210 g / 30 cm³ = 7 g/cm³. Loss in liquid = 210 - 120 = 90 g, so liquid density = 90/30 = 3 g/cm³. The metal density (7) is not 4 times the liquid density (3); and since 7 > 1 the metal sinks in water. So the correct statement is that the metal's density is 7 g/cm³.
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