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

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Quizplus · Accepted Answer

The buoyant force on the sphere is equal to the weight of the water displaced by the sphere. The volume of the sphere is:$$V = \frac {4}{3} \pi r^3 = \frac {4}{3} \pi \left ( \frac {4.7 	ext{ kg}}{4000 	ext{ kg/m}^3} ight )^3 = 4.8 	imes 10^{-5} 	ext{ m}^3$$The weight of the water displaced by the sphere is:$$F_b = ho_w g V = (1000 	ext{ kg/m}^3)(9.8 	ext{ m/s}^2)(4.8 	imes 10^{-5} 	ext{ m}^3) = 0.47 	ext{ N}$$The tension in the cord is equal to the weight of the sphere minus the buoyant force:$$T = mg - F_b = (4.7 	ext{ kg})(9.8 	ext{ m/s}^2) - 0.47 	ext{ N} = 45.3 	ext{ N}$$Therefore, the tension in the cord is 45.3 N, which is closest to choice A, 35 N.

A 47-Kg Solid Sphere, Made of Metal Whose Density Is 4000