Two capillary tubes A and B of the same inter | vedclass

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(B) The height of a liquid column in a capillary tube is given by the formula: $h = \frac{2T \cos 	heta}{r ho g}$.Given that the internal diameters

Vedclass · Accepted Answer

$9:10$

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(B) The height of a liquid column in a capillary tube is given by the formula: $h = \frac{2T \cos 	heta}{r ho g}$.Given that the internal diameters are the same,the radii are equal: $r_A = r_B$.Assuming the angles of contact are nearly equal: $	heta_A = 	heta_B$.Thus,the height $h$ is proportional to $\frac{T}{ho}$,where $T$ is surface tension and $ho$ is density.Therefore,the ratio of the heights is: $\frac{h_A}{h_B} = \frac{T_A}{T_B} 	imes \frac{ho_B}{ho_A}$.Given $\frac{ho_A}{ho_B} = \frac{4}{3}$ and $\frac{T_A}{T_B} = \frac{6}{5}$.Substituting these values: $\frac{h_A}{h_B} = \frac{6}{5} 	imes \frac{3}{4} = \frac{18}{20} = \frac{9}{10}$.So,the ratio is $9:10$.

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