Question

The radii of two columns in a U tube are r1 and r2 when a liquid of density P is filled in it.the level difference of the liquid in the two arms in h.The surface tension of the liquid is

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{From}\mathrm{the}\mathrm{relation}, \\ \mathrm{T}=\frac{\mathrm{hr\rho g}}{2} \\ \mathrm{Therefore},{\mathrm{h}}_1=\frac{2\mathrm{T}}{{\mathrm{r}}_1\mathrm{\rho g}} \\ \mathrm{and}{\mathrm{h}}_2=\frac{2\mathrm{T}}{{\mathrm{r}}_2\mathrm{\rho g}} \\ \mathrm{Now},{\mathrm{h}}_1-{\mathrm{h}}_2=\frac{2\mathrm{T}}{\mathrm{\rho g}}\left(\frac{1}{{\mathrm{r}}_1}-\frac{1}{{\mathrm{r}}_2}\right) \\ \Rightarrow \mathrm{h}=\frac{2\mathrm{T}}{\mathrm{\rho g}}\left(\frac{{\mathrm{r}}_2-{\mathrm{r}}_1}{{\mathrm{r}}_1{\mathrm{r}}_2}\right) \\ \Rightarrow \mathrm{T}=\frac{\mathrm{h\rho g}}{2}\left(\frac{{\mathrm{r}}_1{\mathrm{r}}_2}{{\mathrm{r}}_2-{\mathrm{r}}_1}\right) \\ \mathrm{Where},\mathrm{T}=\mathrm{surface}\mathrm{tension} \end{gathered}$$