Q. Water rises to a height of 10 cm in a capillary tube and mercury falls to a depth of 3.42 cm in the same capillary tube. If the density of mercury and water are $135{^\circ}$ and $0{^\circ}$ respectively, the ratio of surface tension of water and mercury is
A) 1 : 0.15
B) 1 : 3
C) 1 : 6.5
D) 1.5 : 1
Explanation
(c) $h = \frac{2S\cos\theta}{r\ \rho\ g}$ or $S = \frac{h\ r\ \rho\ g}{2\cos\theta}$ or $S \propto \frac{h\ \rho}{\cos\theta}$
$\frac{S_{w}}{S_{Hg}} = \frac{h_{1}}{h_{2}} \times \frac{{\cos\theta}_{2}}{\cos\theta_{1}} \times \frac{1}{13.6}$
$= \frac{10}{( - 3.42)} \times \frac{\cos{135{^\circ}}}{\cos{0{^\circ}}} = \times \frac{1}{13.6}$
$= \frac{10}{3.42} \times \frac{0.707}{13.6} = \frac{1}{6.5}\ $
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.