Question

Two arms of a $U$ tube have unequal diameters $d_1=1.0mm$ and $d_2=1.0cm$. If water (surface tension $7\times {10}^{-2}/m)$ is poured into the tube held in the vertical position, the difference of level of water in the $U$ tube is $\frac{x}{2}cm$. Find $x$ Assume the angle of contact to be zero.

Answer 1

Rise of water is capillary is $H_1=\frac{4T}{\rho g{d}_1}$

so $\Delta H=H_1-H_2=\frac{4T}{\rho g}[\frac{1}{d_1}-\frac{1}{d_2}]$

on putting values is SI unit ,$d_1={10}^{-3}m,d_2={10}^{-2}m$

we get $\Delta H=2.5\times {10}^{-2}mor2.5cm$

so $\frac{x}{2}=2.cm\Rightarrow x=5cm$