If the diameter of a capillary tube is doubled, the capillary rise will be:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 2010
Detailed Explanation
Capillary height in a narrow vertical tube reflects equilibrium between the perimeter surface tension force pulling upward and the weight of the elevated liquid column acting downward.
From the capillary rise equation:
\[ h = \frac{4T\cos\theta}{\rho g d} \;\implies\; h \propto \frac{1}{d} \]
If the diameter is doubled (\(d_2 = 2d_1\)):
\[ h_2 = \frac{4T\cos\theta}{\rho g (2d_1)} = \frac{h_1}{2} \]
Why “Halfed” Is Correct
Because capillary rise is inversely proportional to diameter, doubling \(d\) reduces the capillary rise to half its initial value.
Why the Other Options Are Wrong
- A. Unaffected: Capillary rise changes significantly with tube diameter; it is not unaffected.
- B. Doubled: Capillary rise would double only if diameter were halved.
- D. None of the above: Option (c) correctly identifies that the rise is halved.
Key Point
Capillary rise h ∝ 1/d: doubling tube diameter halves the capillary rise.
Key Concepts for Students
- Jurin's law states that capillary height is inversely proportional to tube bore.
- Surface tension force scales with perimeter (πd), while column weight scales with area (πd²/4).
- For large tubes (d > 12 mm), capillary rise becomes practically negligible.
Practice more: this is question 51 in Properties of Fluid MCQs – Part 4. Try the whole set and check every answer instantly.