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
  1. 2 cm
  2. 6 cm
  3. 4 cm
  4. 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. $h^{\prime}=40 \mathrm{~mm}=4 \mathrm{~cm}$

Asked in: MHT CET 2022 (11 Aug Shift 1)

Practice more Mechanical Properties of Fluids questions on Aicharya