Physics - Fluid Question with Solution | TestHub

When a capillary tube is broken at a height 5 cm, meaning that water will rise to height$5\mathrm{ }\mathrm{cm},$hence$h_2=5\mathrm{ }\mathrm{cm}.$

Since, we know, for capillarity phenomenon$h=\frac{2S\mathrm{c}\mathrm{o}\mathrm{s}\theta }{r\rho g},$where symbols have their usual meaning.

or$\frac{h}{\mathrm{c}\mathrm{o}\mathrm{s}\theta }=$constant

Thus,$\frac{h_1}{\mathrm{c}\mathrm{o}\mathrm{s}{\theta }_1}=\frac{h_2}{\mathrm{c}\mathrm{o}\mathrm{s}{\theta }_2}$

$\Rightarrow \frac{9}{\mathrm{c}\mathrm{o}\mathrm{s}\theta }=\frac{5}{\mathrm{c}\mathrm{o}\mathrm{s}{\theta }_2}$[for glass${\theta }_1=0$]

$\Rightarrow \mathrm{c}\mathrm{o}\mathrm{s}{\theta }_2=\frac{5}{9}$$\left[\because \mathrm{c}\mathrm{o}\mathrm{s}{0}^o=1\right]$

$\therefore {\theta }_2={\mathrm{c}\mathrm{o}\mathrm{s}}^{-1}\left(\frac{5}{9}\right)$