A 4.7-kg solid sphere,made of metal whose density is 4000 kg/ $m ^ { 3 }$ ,hangs by a light cord.When the sphere is immersed in water,what is the tension force the cord exerts on the sphere? The density of water is 1000 kg/m³. A)35 N B)40 N C)46 N D)52 N E)58 N

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Quizplus · Accepted Answer

The tension force is the weight of the sphere minus the buoyant force. The buoyant force is equal to the weight of the water displaced by the sphere. The volume of the sphere is its mass divided by its density, which is 4.7 kg / 4000 kg/m³ = 0.001175 m³. The buoyant force is the volume of the sphere times the density of water times gravity, which is 0.001175 m³ * 1000 kg/m³ * 9.8 m/s² = 11.515 N. The weight of the sphere is its mass times gravity, which is 4.7 kg * 9.8 m/s² = 46.06 N. Therefore, the tension force is 46.06 N - 11.515 N = 34.545 N, approximately 35 N.

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