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 (ρ_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 find the volume of mercury needed, we first determine the volume of the bottle using the displacement method, which is 1.63 × 10^(-4) m^3. Since the bottle needs to just submerge, the weight of the mercury added must equal the buoyant force exerted by the displaced water. The density of mercury is given as 13.6 × 10^3 kg/m^3. Using the formula for buoyant force (weight of displaced fluid), we can calculate the volume of mercury needed. The calculation involves equating the mass of displaced water (volume of the bottle times the density of water, 1000 kg/m^3) to the mass of the mercury added (volume of mercury times the density of mercury, 13.6 × 10^3 kg/m^3). Solving for the volume of mercury gives a result close to 3.75 × 10^(-5) m^3, or 3.75 cm^3 when converted to cm^3 (since 1 m^3 = 10^6 cm^3).

An Empty Spice Bottle Has an Inner Volume of 1