Water rises to a height of $20 \mathrm{~mm}$ in a capillary tube of cross-sectional area $A$. If the area of…
Water rises to a height of $20 \mathrm{~mm}$ in a capillary tube of cross-sectional area $A$. If the area of cross-section of the tube is made $\left(\frac{A}{4}\right)$, then water will rise to a height of
2 cm
6 cm
4 cm
3 cm
Solution
Capillary rise is given by,
$\begin{aligned}
& h=\frac{2 T \cos \theta}{r \rho g} \\
& \Rightarrow h \propto \frac{1}{r} \propto \frac{1}{\sqrt{A}}
\end{aligned}$
If $A$ become one-fourth, $h$ becomes twice.
$h^{\prime}=40 \mathrm{~mm}=4 \mathrm{~cm}$