Physics - Fluid Question with Solution | TestHub

The formula for capillary rise is $h=\frac{2T\cos \theta }{r\rho g}$.

Rearranging the formula, we get $\cos \theta =\frac{hrg}{2T}\rho$.

Since $h$, $r$, $g$, and $T$ are constant for all three liquids, $\cos \theta \propto \rho$.

Given that ${\rho }_1<{\rho }_2<{\rho }_3$, it follows that $\cos {\theta }_1<\cos {\theta }_2<\cos {\theta }_3$.

For capillary rise, the angle of contact $\theta$ is acute ($0\le \theta <90^{\circ }$). In this interval, the cosine function is strictly decreasing.

Therefore, a smaller value of $\cos \theta$ corresponds to a larger angle $\theta$, which gives ${\theta }_1>{\theta }_2>{\theta }_3$.

Answer: ${\theta }_1>{\theta }_2>{\theta }_3$