Question

A capillary tube with inner cross-section in the form of a square of side a is dipped vertically in a liquid of density $\rho$ and surface tension $\sigma$ which wet the surface of capillary tube with angle of contact $\theta$. The approximate height to which liquid will be raised in the tube is : (Neglect the effect of surface tension at the corners of capillary tube)

• A. $\frac{2\sigma cos\theta }{a\rho g}$
• B. $\frac{4\sigma cos\theta }{a\rho g}$
• C. $\frac{8\sigma cos\theta }{a\rho g}$
• D. None of these

Answer 1

The correct option is B $\frac{4\sigma cos\theta }{a\rho g}$

Upward force by capillary tube on top surface of liquid is equal to the product of the perimeter and surface tension.

$F_{up}=4a\sigma \cos \theta$ ... ..(1)

In equilibrium, surface tension force is equal to the weight of the liquid column of height h, h being the height to to which the liquid rises

$W=a^2\rho gh$ .....(2)

Equating (1) and (2)

$4a\sigma \cos \theta =a^2\rho gh$

$\therefore h=\frac{4\sigma \cos \theta }{a\rho g}$