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 * 10-4 m3 of water when fully submerged. What volume of mercury ($\rho$Hg = 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

Question

Quizplus · Accepted Answer

To just submerge, the weight of the bottle with mercury must equal the weight of the displaced water. Calculate the mass of water displaced: $1.63 \times 10^{-4} \, \text{m}^3 \times 1000 \, \text{kg/m}^3 = 0.163 \, \text{kg}$. The mass of the bottle with air is 0.112 kg. The mass of mercury needed is $0.163 \, \text{kg} - 0.112 \, \text{kg} = 0.051 \, \text{kg}$. The volume of mercury needed is $0.051 \, \text{kg} / (13.6 \times 10^3 \, \text{kg/m}^3) = 3.75 \times 10^{-6} \, \text{m}^3 = 3.75 \, \text{cm}^3$.

An Empty Spice Bottle Has an Inner Volume of 1 ρ\rhoρ

An Empty Spice Bottle Has an Inner Volume of 1 $\rho$