Water rises to a height of 20 mm in a capill | vedclass

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(A) The height of capillary rise $h$ is given by the formula $h = \frac{2T \cos 	heta}{r ho g}$,where $T$ is surface tension,$	heta$ is the angle

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$60$

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(A) The height of capillary rise $h$ is given by the formula $h = \frac{2T \cos 	heta}{r ho g}$,where $T$ is surface tension,$	heta$ is the angle of contact,$r$ is the radius,$ho$ is the density,and $g$ is the acceleration due to gravity. From this formula,we see that $h \propto \frac{1}{r}$. Given that the initial height $h = 20 \ mm$ and the new radius $r' = \frac{r}{3}$. Using the proportionality $h' r' = h r$,we get: $h' = h \left( \frac{r}{r'} ight) = 20 	imes \left( \frac{r}{r/3} ight) = 20 	imes 3 = 60 \ mm$.

Water rises to a height of $20 \ mm$ in a capillary tube. If the radius of the capillary tube is made $\frac{1}{3}rd$ of its previous value,what is the new height of the capillary rise (in $mm$)?

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