Question

Three liquids of densities 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. $\pi > \theta_1 > \theta_2 > \theta_3 > \frac{\pi}{2}$

Answer 1

Answer: (B)

$h = \frac{2T \cos\theta_{c}}{r \rho g} = $ same
$ \cos \theta_{c} \propto \rho$
$ \rho_{1} > \rho_{2} > \rho_{3} $
$\cos\theta c_{1} > \cos \theta c_{2} > \cos \theta_{c_3} $
$ 0 \le \theta_{c_1} < \theta_{c_2} < \theta_{c_3} < \frac{\pi}{2} $