Water rises in a capillary tube of radius ' $r$ ' to a height ' $h$ '. The mass of water in a capillary is '…

Water rises in a capillary tube of radius ' $r$ ' to a height ' $h$ '. The mass of water in a capillary is ' $m$ '. The mass of water will rise in a capillary tube of radius $\frac{r}{3}$ will be
  1. $3m$
  2. $\frac{\mathrm{m}}{3}$
  3. $m$
  4. $\frac{2 \mathrm{~m}}{3}$

Solution

$\begin{aligned} & \mathrm{h} \propto \frac{1}{\mathrm{r}} \quad \therefore \frac{\mathrm{h}_2}{\mathrm{~h}_1}=\frac{\mathrm{r}_1}{\mathrm{r}_2}=3 \\ & \therefore \mathrm{h}_2=3 \mathrm{~h}_1 \\ & \mathrm{~m}_1=\mathrm{h}_1 \pi \mathrm{r}_1^2 \rho, \mathrm{m}_2=\mathrm{h}_2 \pi \mathrm{r}_2^2 \rho \\ & \therefore \frac{\mathrm{m}_2}{\mathrm{~m}_1}=\frac{\mathrm{h}_2}{\mathrm{~h}_1}\left(\frac{\mathrm{r}_2}{\mathrm{r}_1}\right)^2=3 \times\left(\frac{1}{3}\right)^2=\frac{1}{3} \\ & \therefore \mathrm{m}_2=\frac{\mathrm{m}_1}{3}\end{aligned}$ .

Asked in: MHT CET 2021 (22 Sep Shift 1)

Practice more Mechanical Properties of Fluids questions on Aicharya