Question

The surface tension of water is determined by capillary rise method in the laboratory. The principle involved is (symbols have their usual meanings):

• A. $T=\frac{r}{3}(h+\frac{r}{3})dg$
• B. $T=\frac{r}{4}(h+\frac{r}{2})dg$
• C. $T=\frac{r}{2}(h+\frac{r}{3})dg$
• D. $T=\frac{r}{2}(\frac{h}{3}+r)dg$

Answer 1

The correct option is C $T=\frac{r}{2}(h+\frac{r}{3})dg$

In cases where, the volume of water inside the meniscus is not included,

h = $\frac{2Tcos\theta }{\rho gr}$

However, if you include the volume of water within the meniscus,

V = Volume of cylinder of radius r and height h - volume of hemisphere of radius r

V = $\pi r^3-2/3\pi r^3$

V = $\frac{1}{3}\pi r^3$

Total volume of the liquid = $\pi r^{2}h+\frac{1}{3}\pi r^3$

V = $\pi r^2(h+r/3)$

Weight of water = $\pi r^2(h+r/3)dg$

This should be equal to the total upward force because of surface tension.

$T\times 2\pi r=\pi r^2(h+r/3)dg$

Hence, $T=\frac{r}{2}(h+r/3)dg$