# Obtain by the method of dimensional analysis an expression for the surface tension of a liquid rising in a capillary tube. Assume that the surface tension depends on mass m of the liquid, pressure P of the liquid and radius r of the capillary tube. The constant $k = \large\frac{1}{2}$.

$\sigma = \large\frac{1}{2}$$m^{\circ}p^1r^1 [ \because k = \large\frac{1}{2}$$ ( given ) ] \: or\: \sigma = \large\frac{pr}{2}$