A capillary tube (P) is dipped in water. Another identical tube (Q) is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?

Explanation

The capillary rise is given by, h=2Tcosθ/ρrg ...(i). The soap solution and water both wet the side of the capillary tube. ⇒The angle of contact for soap solution with glass, and the angle of contact for water with glass will both be acute (θ<90∘). Hence, the shape of the meniscus for water and soap both will be concave (concavity being higher for water-meniscus) Since soap solution has a greater tendency to stick to the wall of the tube, the angle of contact for soap-solution will be lesser. i.e θsoap<θwater The surface tension of soap solution is reduced to a much higher extent (i.e approx 3 times lesser then that of water), due to presence of surfactants. i.e Tsoap<Twater The increase in value of cosθ for soap solution will be lesser compared to the reduction in its surface tension, because both solutions are wetting in nature. Hence from Eq.(i) due to dominance of decrease in surface tension, hsoap<hwater The value of height h to which the liquid rises in the capillary tube will be less for soap solution than for water. ∴ Higher rise of liquid in A with concave meniscus, represents water.