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  4. The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, 5 cm. If the tube is dipped in a similar manner in another liquid B of surface tension and density double the values of liquid A, the height of liquid column raised in liquid B would be m.

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Q. The height of liquid column raised in a capillary tube of certain radius when dipped in liquid $A$ vertically is, $5 \,cm$. If the tube is dipped in a similar manner in another liquid $B$ of surface tension and density double the values of liquid $A$, the height of liquid column raised in liquid $B$ would be ______$m$.

JEE MainJEE Main 2023Mechanical Properties of Fluids

Solution:

$ h =\frac{2 S \cos \theta}{ r \rho g }$
$\therefore \frac{ h _1}{ h _2} =\frac{ S _1}{ S _2} \frac{\rho_2}{\rho_1} $
$\frac{5}{ h _2} =\left[\frac{1}{2}\right]\left[\frac{2}{1}\right] \Rightarrow h _2=5 cm =0.05 m$
$\{$Info about angle of contact not there so most appropriate is 3 $\}$