Question

The maximum diameter that a capillary tube can have to ensure that a capillary rise of at least 6 mm is achieved when the tube is dipped into a body of liquid with surface tension \( = 0.08 \, \text{N/m} \) and density \( = 900 \, \text{kg/m}^3 \) is ...........

• A. 3 mm
• B. 6 mm
• C. 5 mm
• D. 8 mm

Hint:

Capillary rise is inversely proportional to tube diameter. Smaller diameter means higher rise. Rearranging the formula gives a quick way to find the max diameter for a required height.

Answer 1

The Correct Option is B

The height of capillary rise is given by the formula:
\[ h = \frac{4 \sigma}{\rho g d} \]
Solving for diameter \( d \):
\[ d = \frac{4 \sigma}{\rho g h} \]
Substitute the given values:
\[ \sigma = 0.08 \, \text{N/m}, \quad \rho = 900 \, \text{kg/m}^3, \quad g = 9.81 \, \text{m/s}^2, \quad h = 6 \, \text{mm} = 0.006 \, \text{m} \]
\[ d = \frac{4 \times 0.08}{900 \times 9.81 \times 0.006} \approx \frac{0.32}{52.974} \approx 0.00604 \, \text{m} = 6.04 \, \text{mm} \]
So the maximum allowable diameter is approximately \( \boxed{6 \, \text{mm}} \).