Question

Water rises to a height of 10 cm in capillary tube and mercury falls to a depth of 3.1 cm in the same capillary tube. If the density of mercury is 13.6 and the angle of contact for mercury is ${135}^0$, the approximate ratio of surface tension of water and mercury is:

• A. 1:0.15
• B. 1:3
• C. 1:6
• D. 1.5:1

Answer 1

Answer: (C)

1:6

$h=\frac{2\sigma cos\theta }{rpg}$

$\Rightarrow \sigma \propto \frac{h\rho }{cos\theta }$

$\Rightarrow \frac{{\sigma }_w}{{\sigma }_m}=\frac{h_w{\rho }_w}{cos{\theta }_w}\times \frac{cos{\theta }_m}{h_m{\rho }_m}=\frac{10\times 1}{cos{0}^0}\times \frac{cos{135}^0}{-3.1\times 13.6}$

$=\frac{10\times (-0.707)}{-3.1\times 13.6}\approx \frac{1}{6}$