Water rises to a height 3 cm in a capillary tube. If cross-sectional area of capillary tube is reduced to 1/ 3 r d of its initial area then water will rise to a height of

Question

TestHub · Accepted Answer

The height of water in a capillary tube is given by $h = \frac{2 T cos θ}{ρ g r}$

This implies $h \propto \frac{1}{r}$

Given that the cross-sectional area is reduced to $\frac{1}{3}$ of its initial value:

$A_{2} = \frac{A _{1}}{3}$

$π r_{2}^{2} = \frac{π r _{1}^{2}}{3}$

$r_{2} = \frac{r _{1}}{3}$

Using the relation $h_{1} r_{1} = h_{2} r_{2}$ :

$h_{2} = h_{1} \frac{r _{1}}{r _{2}}$

$h_{2} = 3 \times 3 = 33$ cm

Answer: $33$ cm

Physics - Fluid Question with Solution | TestHub

Options:

Doubts & Discussion