A 4.7-kg solid sphere,made of metal whose density is 4,000 kg/ m³. 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 tension in the cord is reduced by the buoyant force acting on the sphere when it is immersed in water. The buoyant force equals the weight of the water displaced by the sphere. First, find the volume of the sphere using its mass (m = 4.7 kg) and the density of the metal ($\rho_{metal} = 4000 \, \text{kg/m}^3$):$$V = \frac{m}{\rho_{metal}} = \frac{4.7}{4000} \, \text{m}^3.$$Then, calculate the weight of the water displaced, which has the same volume, using the density of water ($\rho_{water} = 1000 \, \text{kg/m}^3$) and gravity (g = 9.8 m/s$^2$):$$F_{buoyant} = \rho_{water} \cdot V \cdot g = 1000 \cdot \frac{4.7}{4000} \cdot 9.8 \, \text{N}.$$Finally, subtract the buoyant force from the original weight of the sphere to find the tension in the cord:$$T = mg - F_{buoyant} = 4.7 \cdot 9.8 - 1000 \cdot \frac{4.7}{4000} \cdot 9.8 = 46.06 \, \text{N} - 11.555 \, \text{N} = 34.505 \, \text{N}.$$Rounded to the nearest whole number, the tension is approximately 35 N.

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