An empty spice bottle has an inner volume of 1.31 × 10⁻⁴ m³. It has a mass of 112 g when filled with air, and it displaces 1.63 × 10⁻⁴m³ of water when fully submerged. What volume of mercury (ρHg = 13.6 × 10³ kg/m³) must be added to the empty bottle so that it will just submerge? A)3.75 cm³ B)12.0 cm³ C)101 cm³ D)147 cm³ E)237 cm³

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Quizplus · Accepted Answer

The correct answer is A.The mass of the air in the bottle is:$$m_{air} = ho_{air} V_{bottle} = (1.29 	imes 10^{-3} 	ext{ kg/m}^3)(1.31 	imes 10^{-4} 	ext{ m}^3) = 1.69 	imes 10^{-7} 	ext{ kg}$$The mass of the water displaced by the bottle is:$$m_{water} = ho_{water} V_{displaced} = (1000 	ext{ kg/m}^3)(1.63 	imes 10^{-4} 	ext{ m}^3) = 0.163 	ext{ kg}$$The mass of the mercury that must be added to the bottle is:$$m_{mercury} = m_{water} - m_{air} = 0.163 	ext{ kg} - 1.69 	imes 10^{-7} 	ext{ kg} = 0.163 	ext{ kg}$$The volume of the mercury that must be added to the bottle is:$$V_{mercury} = \frac{m_{mercury}}{ho_{mercury}} = \frac{0.163 	ext{ kg}}{13.6 	imes 10^3 	ext{ kg/m}^3} = 1.20 	imes 10^{-5} 	ext{ m}^3 = 12.0 	ext{ cm}^3$$

An Empty Spice Bottle Has an Inner Volume of 1