Question

a glass rod of radiusof radius 1 mm is inserted symettrically into a glass capillary tube with inside radius 2 mm . then the whole arrangement is brought in contact of the surface of water . surfae tension of water is 7*10^ -2 N/m . to what height will the water rise.(theta -0 deg}

(ans 1.4 cm)

Answer 1

$$\begin{gathered} {\text{Total upward Force due to surface Tension , F= T ( 2πr}}_1+2\pi r_2).......(1) \\ {\text{where T is surface tension of water=7×10}}^{\text{-2}}\text{N /m} \\ {\text{r}}_1\text{is radius of the glass rod =1mm} \\ {\text{r}}_2\text{is the radius of the capillary tube=2mm} \\ \text{Weight of the liquid Column, W=h}\left[{{\text{πr}}_2}^2-{{\text{πr}}_1}^2\right]\text{dg}.......(2) \\ \text{Now on equating (1) and (2) equations , we get}, \\ \text{hπ}\left({\text{r}}_1+r_2\right)\left(r_2-r_1\right)dg=\text{2Tπ}(r_1+r_2) \\ {\text{where d is density of the water = 10}}^{3}kg/m^3 \\ \text{g is the acceleration due to gravity}=10m/s^2 \\ Soh=\frac{2T}{\left(r_2-r_1\right)dg} \\ =\frac{2\times {\mathrm{7\times 10}}^{\text{-2}}}{(2-1)\times {10}^{-3}\times 10\times {10}^3} \\ =14\times {10}^{-3}m=1.4\times {10}^{-2}m=1.4cm \end{gathered}$$