Question

The radii of the columns in U- tube are $r_1$ and $r_2$. when a liquid of density p (angle of contact is $0^{\circ }$) is filled in it in the level difference of liquid in two arms is h. The surface tension of liquid is : (g= acceleration due to gravity)

Answer 1

Rise of liquid in the capillare tube $n^{\prime }$

given m

$h=\frac{2T}{rpg}$

$h_1$ is height of tube of radius $r_1$

$h_2$ is height of tube of radius $r_2$

$h_1=\frac{2T}{r_{1}pg}$

$h_2=\frac{2T}{r_{2}pg}$

$h=h_1-h_2=\frac{2T}{r_{1}pg}-\frac{2T}{r_{2}pg}=\frac{2T}{pg}[\frac{1}{r_1}-\frac{1}{r_2}]$

$h=\frac{2T}{pg}\left[\frac{r_2-r_1}{r_1{r}_2}\right]$

$\therefore T=\frac{hpg{r}_1{r}_2}{2(r_2-r_1)}$