Question

A boy can reduce the pressure in his lungs to 750 mm of mercury. Using a straw he can drink water from a glass upto the maximum depth of (atmospheric pressure = 760 mm of mercury; density of mercury = \(13.6 \text{ gcm}^{-3}\))

• A. \(13.6 \text{ cm}\)
• B. \(9.8 \text{ cm}\)
• C. \(10 \text{ cm}\)
• D. \(76 \text{ cm}\)
• E. \(1.36 \text{ cm}\)

Hint:

To find the height of a liquid column that exerts the same pressure as another, use the inverse ratio of densities: \(h_1 \rho_1 = h_2 \rho_2\). Water is 13.6 times less dense than mercury, so the column will be 13.6 times taller!

Answer 1

The Correct Option is A

Concept: The ability to suck liquid through a straw depends on the pressure difference (\(\Delta P\)) between the atmosphere and the lungs.
• Pressure difference: \(\Delta P = P_{atm} - P_{lung}\)
• Pressure of a liquid column: \(P = h \rho g\)
• Equating pressures: \(h_w \rho_w g = h_{Hg} \rho_{Hg} g\)

Step 1: Calculate the pressure difference in terms of Mercury column.
\[ \Delta P = 760 \text{ mm} - 750 \text{ mm} = 10 \text{ mm of Hg} = 1 \text{ cm of Hg} \]

Step 2: Convert the Mercury column height to Water column height.
Since \(P = h_w \rho_w g = h_{Hg} \rho_{Hg} g\), we have: \[ h_w = \frac{h_{Hg} \rho_{Hg}}{\rho_w} \] Given \(\rho_{Hg} = 13.6 \text{ g/cm}^3\) and \(\rho_{w} = 1 \text{ g/cm}^3\): \[ h_w = \frac{1 \text{ cm} \times 13.6}{1} = 13.6 \text{ cm} \]