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  4. Two capillary tubes of same diameter are put vertically one each in two liquids whose relative densities are 0.8 and 0.6 and surface tensions are 70 and 40 dyne/ cm respectively. The ratio of heights of liquids in the tubes ( h 1/ h 2) is

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Q. Two capillary tubes of same diameter are put vertically one each in two liquids whose relative densities are 0.8 and 0.6 and surface tensions are 70 and 40 dyne/ $cm$ respectively. The ratio of heights of liquids in the tubes $\frac{ h _{1}}{ h _{2}}$ is

Mechanical Properties of Fluids

Solution:

$r=\frac{2 S \cos \theta}{h \rho g} $
$\Rightarrow D=\frac{4 S \cos \theta}{h \rho g}=\frac{4 S \cos \theta \rho_{w}}{h \times \rho_{e} \times g}$
$\therefore \frac{h_{1}}{h_{2}}=\frac{S_{1}}{S_{2}} \times \frac{\rho_{\ell_{2}}}{\rho_{\ell_{1}}}=\frac{70}{40} \times \frac{0.6}{0.8}=\frac{42}{32}$
$\therefore \frac{h_{1}}{h_{2}}=\frac{21}{16}$