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

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

Solution

The height of water column in a capillary tube is given by $\mathrm{h}=\frac{2 \mathrm{~T} \cos \theta}{\mathrm{perg}}$ From eqs. (i) and (ii), we get $\begin{aligned} & m \propto r^2 \times \frac{1}{r} \\ & m \propto r \\ & \Rightarrow \frac{m^{\prime}}{m}=\frac{\frac{r}{4}}{r} \Rightarrow m^{\prime}=\frac{m}{4}\end{aligned}$ :

Asked in: MHT CET 2022 (07 Aug Shift 2)

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