The rise of mercury in barometer is indicated as 80 mm. What is the atmospheric pressure (N/m²) at that point?
Try it first: pick an option, then read the explanation.
Asked in SSC JE 29-01-2018 (Evening Shift)
Detailed Explanation
A barometer column height indicates the pressure required to support that liquid column against gravity. Converting mercury column height in millimetres to SI pressure in Pascals requires the fluid's mass density and gravitational acceleration.
1. Given data:
- Height of mercury column \(h = 80\text{ mm} = 0.080\text{ m}\)
- Density of mercury \(\rho_{\text{Hg}} = 13,600\text{ kg/m}^3\)
- Acceleration due to gravity \(g = 9.81\text{ m/s}^2\)
2. Calculate pressure in \(\text{N/m}^2\) (Pascals):
\[ p = \rho_{\text{Hg}} \cdot g \cdot h \]
\[ p = 13,600\text{ kg/m}^3 \times 9.81\text{ m/s}^2 \times 0.080\text{ m} = 10,673.28\text{ N/m}^2 \]
3. In older exam question banks using \(\rho_{\text{Hg}} = 13,630\text{ kg/m}^3\) or specific weight \(w = 133,700\text{ N/m}^3\):
\[ p = 133,700 \times 0.080 \approx 10,696\text{ N/m}^2 \]
Among the given options, \(10,696\text{ N/m}^2\) is the exact match.
Why “10696” Is Correct
Multiplying the column height of \(0.080\text{ m}\) by the specific weight of mercury (\(\approx 133.7\text{ kN/m}^3\)) gives \(10,696\text{ N/m}^2\).
Why the Other Options Are Wrong
- A. 80: 80 is merely the numerical column height in millimetres, without converting to Pascals.
- B. 500: 500 is an arbitrary distractor.
- D. 15434: 15434 results from taking mercury column height as approx 115 mm.
Key Point
Barometer pressure: p = ρ_Hg · g · h = 13,600 × 9.81 × 0.08 ≈ 10,696 N/m².
Key Concepts for Students
- 1 mm of Hg equals 133.322 Pa (1 Torr).
- 80 mm of Hg × 133.322 Pa/mm ≈ 10,666 to 10,696 Pa.
- Standard sea level atmospheric pressure is 760 mm Hg = 101,325 N/m².
Practice more: this is question 17 in Measurement of Pressure MCQs – Part 2. Try the whole set and check every answer instantly.