Three liquids of the same density but different surface tensions $T_1, T_2$, and $T_3$ (where $T_1

Question

Three liquids of the same density but different surface tensions $T_1, T_2$, and $T_3$ (where $T_1 > T_2 > T_3$) rise to the exact same height in three identical capillary tubes. If their angles of contact are $	heta_1, 	heta_2$, and $	heta_3$ respectively (all being acute), then the correct relation is

Professor PC Thomas Classes · Answer

(b) : The formula for capillary rise is $h = \frac{2T \cos heta}{r ho g}$. For a given height $h$, radius $r$, and density $ ho$, the product $T \cos heta$ must be constant. Thus, $T_1 \cos heta_1 = T_2 \cos heta_2 = T_3 \cos heta_3$. Since we are given $T_1 > T_2 > T_3$, it must follow that $\cos heta_1 < \cos heta_2 < \cos heta_3$ to keep the product constant. For acute angles ($0 \leq heta < 90^{\circ}$), a smaller cosine value corresponds to a larger angle. Therefore, $ heta_1 > heta_2 > heta_3$.