If mercury in a barometer is replaced by water, the height of 3.75 cm of mercury will be following cm of water.............
Try it first: pick an option, then read the explanation.
Asked in SSC JE 4 MARCH 2017 Morning Shift
Detailed Explanation
Because mercury is 13.6 times denser than water, a given column height of mercury exerts a hydrostatic pressure 13.6 times greater than an equal height of water.
1. State the given data:
- Height of mercury column \(h_{\text{Hg}} = 3.75\text{ cm}\)
- Specific gravity of mercury \(S_{\text{Hg}} = 13.6\)
- Specific gravity of water \(S_w = 1.0\)
2. Equate the hydrostatic pressure developed by both liquids:
\[ \rho_w g h_w = \rho_{\text{Hg}} g h_{\text{Hg}} \]
3. Simplify using specific gravities:
\[ h_w \cdot S_w = h_{\text{Hg}} \cdot S_{\text{Hg}} \]
\[ h_w = h_{\text{Hg}} \times 13.6 = 3.75\text{ cm} \times 13.6 = 51.0\text{ cm} \]
Why “51 cm” Is Correct
Multiplying the mercury column height of \(3.75\text{ cm}\) by the specific gravity of mercury (\(13.6\)) gives an equivalent water column height of exactly \(51.0\text{ cm}\).
Why the Other Options Are Wrong
- B. 50 cm: 50 cm results from using S_Hg ≈ 13.33 (3.75 × 13.33 = 50).
- C. 52 cm: 52 cm results from using S_Hg ≈ 13.87.
- D. 52.2 cm: 52.2 cm results from using S_Hg = 13.92.
Key Point
Equivalent water head: h_water = h_Hg × S_Hg = 3.75 × 13.6 = 51 cm.
Key Concepts for Students
- Specific gravity of mercury at standard conditions is 13.6.
- A full standard atmospheric column of 76 cm Hg corresponds to 76 × 13.6 = 1033.6 cm = 10.34 m of water.
- Water barometers are impractically tall (over 10 metres high) compared to compact 1-metre mercury barometers.
Practice more: this is question 28 in Measurement of Pressure MCQs – Part 2. Try the whole set and check every answer instantly.