Q. Three liquids of densities $\rho_1$, $\rho_2$ and $\rho_3$ (with $\rho_1 > \rho_2 > \rho_3$), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact $\theta_1$, $\theta_2$ and $\theta_3$ obey
A) $\frac{\pi}{2} > \theta_1 > \theta_2 > \theta_3 \geq 0$
B) $0 \leq \theta_1 < \theta_2 < \theta_3 < \frac{\pi}{2}$
C) $\frac{\pi}{2} < \theta_1 < \theta_2 < \theta_3 < \pi$
D) $\pi > \theta_1 > \theta_2 > \theta_3 > \frac{\pi}{2}$
Explanation
[Solution] $h = \frac{2T\cos\theta}{\rho gr}$; equal h means $\cos\theta \propto \rho$, so the densest liquid has the smallest angle, all acute. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.