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 in the cord? The density of water is 1000 kg/m³. A) 35 N B) 40 N C) 46 N D) 52 N E) 58 N

Question

Quizplus · Accepted Answer

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

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