A simple barometer is constructed using a liquid Q 1 of density 16.2 g/cm^ 3 . Calculate the least lenth of…

Analyze the question: A barometer uses a liquid of density 16.2 g/cm³ instead of mercury. We need the height of this liquid that balances a pressure of 1.5 atm, since the tube must be at least that long.

Concept: Pressure from a liquid column is P = ρgh. Two liquids balancing the same pressure satisfy:

ρ₁h₁ = ρ₂h₂

Solution:

1. Pressure in terms of mercury: 1.5 atm = 1.5 × 76.0 = 114 cm of mercury

2. Equate pressures: ρ_Q × h_Q = ρ_Hg × h_Hg 16.2 × h_Q = 13.6 × 114

3. Solve for h_Q: h_Q = (13.6 × 114) / 16.2 = 1550.4 / 16.2 ≈ 95.7 cm

4. Convert to mm: 95.7 cm = 957 mm

Check: The liquid is denser than mercury, so the column should be shorter than 114 cm. 95.7 cm fits this.

Answer: The least length of the tube is about 957 mm, which is option B.

Tip: For barometer problems with different liquids, always use ρ₁h₁ = ρ₂h₂. A denser liquid gives a shorter column, and a lighter liquid gives a longer one. This lets you quickly eliminate unreasonable options.