Question

Water rises to a height of 10cm in a capillary tube and mercury falls to a depth of 3.42 cm in the same capillary tube. If the density of mercury is 13.6 and the angle of contact of mercury and water are 135° and 0° respectively, then the ratio of surface tensions of water and mercury is

• A. (a) 1 : 0.15
• A. (b) 1 : 3
• A. (c) 1 : 6.5
• A. (d) 1.5 : 1

Answer 1

(c)

h = $\frac{2S\cos\theta}{r\rho g}$

or S = $\frac{hr\rho g}{2\cos\theta}$

or S ∝ $\frac{h\rho}{\cos\theta}$

$\frac{S_{W}}{S_{Hg}} = \frac{h_{1}}{h_{2}} \times \frac{\cos\theta_{2}}{\cos\theta_{1}} \times \frac{\rho_{1}}{\rho_{2}}$Putting the values,

we obtain 1 : 6.5

Hence, (C) is the correct choice.