A 6.1-kg solid sphere, made of metal whose density is 2600 kg/ m³, is suspended by a cord. When the sphere is immersed in a liquid of unknown density, the tension in the cord is 26 N. Find the density of the liquid. A) 1500 kg/m³ B) 1400 kg/m³ C) 1300 kg/m³ D) 1200 kg/m³ E) 1100 kg/m³

Question

Quizplus · Accepted Answer

The buoyant force on the sphere is equal to the weight of the liquid displaced by the sphere. The weight of the liquid displaced is equal to the difference between the weight of the sphere in air and the tension in the cord. Therefore, the density of the liquid is equal to the weight of the liquid displaced divided by the volume of the liquid displaced. The volume of the liquid displaced is equal to the volume of the sphere, which is (4/3)πr^3, where r is the radius of the sphere. The radius of the sphere can be found from the density of the sphere and its mass. The mass of the sphere is 6.1 kg and the density of the sphere is 2600 kg/m^3. Therefore, the radius of the sphere is 0.1 m. The volume of the liquid displaced is therefore (4/3)π(0.1 m)^3 = 0.00419 m^3. The weight of the liquid displaced is equal to the difference between the weight of the sphere in air and the tension in the cord, which is 6.1 kg * 9.8 m/s^2 - 26 N = 34.78 N. Therefore, the density of the liquid is 34.78 N / 0.00419 m^3 = 8300 kg/m^3.

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