Question

A U tube is made of two capillary tubes of diameter $0.5\text{mm}$ and $1.0\text{mm}$ respectively. It contains $H_{2}O$. Find the difference in the levels of water between the two arms of the U tube. (Surface tension of $H_{2}O=75\text{dynes/cm}$ and $g=980{\text{cm/s}}^2$).

• A. $2.4\text{cm}$
• B. $2.6\text{cm}$
• C. $2.8\text{cm}$
• D. $3\text{cm}$

Answer 1

The correct option is D $3\text{cm}$

Capillary rise in a tube is given by
$h=\frac{2T}{\rho rg}$

Hence, difference in levels of water between the two tubes
$\Delta h=\frac{2T}{\rho g}[\frac{1}{r_1}-\frac{1}{r_2}]$
where $r_1=0.25\text{mm},r_2=0.5\text{mm}$

Given, $T=75{\text{dynes/cm}}^2$ & $g=980{\text{cm/s}}^2$
We know, density of water $\rho =1{\text{g/cm}}^3$

$\Rightarrow \Delta h=\frac{2\times 75}{1\times 980}[\frac{1}{0.025}-\frac{1}{0.05}]\approx 3\text{cm}$