Two capillary tubes A and B of the same internal diameter are kept vertically in two different liquids whose densities are in the ratio 4 : 3 . If the surface tensions of these two liquids are in the

Question

Two capillary tubes A and B of the same internal diameter are kept vertically in two different liquids whose densities are in the ratio 4 : 3 . If the surface tensions of these two liquids are in the ratio 6 : 5 , then the ratio of rise of liquid in capillary A to that in B is (assume their angles of contact are nearly equal)

TestHub · Accepted Answer

The formula for capillary rise is given by $h = \frac{2 T cos θ}{r ρ g}$

Since the internal diameters are the same, $r_{A} = r_{B}$ . The angles of contact are nearly equal, so $cos θ_{A} = cos θ_{B}$ .

The ratio of capillary rise is:

$\frac{h _{A}}{h _{B}} = \frac{T _{A}}{T _{B}} \times \frac{ρ _{B}}{ρ _{A}}$

Given $\frac{T _{A}}{T _{B}} = \frac{6}{5}$ and $\frac{ρ _{A}}{ρ _{B}} = \frac{4}{3}$

$\frac{h _{A}}{h _{B}} = \frac{6}{5} \times \frac{3}{4} = \frac{18}{20} = \frac{9}{10}$

Answer: $9 : 10$

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