Question

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

• A. $5/4$
• B. $2/3$
• C. $21/16$
• D. $16/21$

Answer 1

Answer: (C)

$r=\frac{2S\cos \theta }{h\rho g}$
$\Rightarrow D=\frac{4S\cos \theta }{h\rho g}=\frac{4S\cos \theta {\rho }_w}{h\times {\rho }_e\times g}$
$\therefore \frac{h_1}{h_2}=\frac{S_1}{S_2}\times \frac{{\rho }_{{\ell }_2}}{{\rho }_{{\ell }_1}}=\frac{70}{40}\times \frac{0.6}{0.8}=\frac{42}{32}$
$\therefore \frac{h_1}{h_2}=\frac{21}{16}$