Question

Which one of the following expresses the height of rise or fall of a liquid in a capillary tube?

Where,
w = Specific weight of the liquid
$\alpha$ = Angle of contact of the liquid surface
$\sigma$ = Surface tension

• A. $\frac{4wd}{\sigma cos\alpha }$
• B. $\frac{\sigma cos\alpha }{4w\alpha }$
• C. $\frac{4\sigma cos\alpha }{wd}$
• D. $\frac{wd}{2\sigma cos\alpha }$

Answer 1

The correct option is C $\frac{4\sigma cos\alpha }{wd}$

Let us suppose that the level of liquid has risen (or fallen) by 'h' above (or below) the general liquid surface when a tube of diameter 'd' is inserted in the liquid. For equilibrium of vertical forces acting on the mass of liquid lying above (or below) the general liquid level, the weight of liquid column 'h' (or the total internal pressure in the case of capillary depression ) must be balanced by the force, at surface of the liquid, due to surface tension $\sigma$. Thus, equating these two forces we have



$\frac{w\pi d^2}{4}\times h=\pi d\sigma cos\theta \Rightarrow h=\frac{4\sigma cos\theta }{wd}$