Water rises to a height of 15 ,mm in a capill | vedclass

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Question

(A) The height $h$ to which a liquid rises in a capillary tube is given by the formula $h = \frac{2T \cos 	heta}{r ho g}$, where $r$ is the radius

Vedclass · Accepted Answer

$15 \sqrt{3} 	imes 10^{-3} \,m$

Vedclass · Answer

(A) The height $h$ to which a liquid rises in a capillary tube is given by the formula $h = \frac{2T \cos 	heta}{r ho g}$, where $r$ is the radius of the tube.This implies $h \propto \frac{1}{r}$.Since the cross-sectional area $A = \pi r^2$, we have $r = \sqrt{\frac{A}{\pi}}$, which means $r \propto \sqrt{A}$.Substituting this into the proportionality, we get $h \propto \frac{1}{\sqrt{A}}$.Given $h_1 = 15 \,mm = 15 	imes 10^{-3} \,m$ for area $A_1 = A$.For the new area $A_2 = A / 3$, we have the ratio $\frac{A_1}{A_2} = 3$.Using the relation $\frac{h_2}{h_1} = \sqrt{\frac{A_1}{A_2}}$, we get $\frac{h_2}{h_1} = \sqrt{3}$.Therefore, $h_2 = h_1 	imes \sqrt{3} = 15 	imes 10^{-3} 	imes \sqrt{3} \,m = 15 \sqrt{3} 	imes 10^{-3} \,m$.

Water rises to a height of $15 \,mm$ in a capillary tube having cross-sectional area $A$. If the cross-sectional area of the tube is made $A / 3$, then the water will rise to a height of:

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