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A capillary tube A is dipped in water. Another identical tube B is dipped in a soap-water solution. Each choice below describes a sketch of the two tubes standing side by side in their beakers, with the risen column shown in each. Which of them shows the relative nature of the liquid columns in the two tubes?

Asked in AIEEE 2008 · Capillary rise

• (1) Both columns rise right to the top of the tubes.
• (2) The column in A is very low, while that in B is high.
• (3) Both columns are equally high.
• (4) The column in A is higher than the column in B.

Step-by-step solution

Why the other options are wrong

• (1) comes from would need each liquid to fill its whole tube, which happens only when the tube is shorter than the rise the liquid can support; the tubes here are long enough to show the rise, and this sketch also hides the very difference being asked about.
• (2) comes from has the effect backwards — it treats soap as raising the surface tension of water. Soap is a surfactant: it lowers T, which is exactly why soapy water spreads and wets so readily.
• (3) comes from assumes dissolving soap leaves T unchanged; if that were so the columns would indeed match, since r, ρ and θ are effectively the same in the two tubes.

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