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MHT CET · Physics · Mechanical Properties of Fluids

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. A \(3m\)
  2. B \(\frac{\mathrm{m}}{3}\)
  3. C \(m\)
  4. D \(\frac{2 \mathrm{~m}}{3}\)
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Answer & Solution

Correct Answer

(B) \(\frac{\mathrm{m}}{3}\)

Step-by-step Solution

Detailed explanation

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