Question

Two capillary tubes are dipped in the liquid of densities in the ratio $5:2$ and the heights of liquids in the two tubes are $2cm$ and $3cm$ respectively. If surface tensions of liquids are $75$ and $70dyne/cm$ respectively. Assume the angles of contacts are same then ratio of the radii is

• A. $7:5$
• B. $5:7$
• C. $14:15$
• D. $9:14$

Answer 1

Answer: (D)

$9:14$

By using rise in capillary tube formula, $h=\frac{2T\cos \theta }{\rho gr}$

where, $h$ is rise of water in capillary
$T$ is surface tension of water
$\rho$ is density of water
$g$ is acceleration due to gravity
$r$ is radius of capillary

So, $h_A=\frac{2T_A\cos \theta }{{\rho }_A{r}_{A}g}=2$ ................(1)

$h_A=\frac{2T_B\cos \theta }{{\rho }_B{r}_{B}g}=2$ ................(2)
Dividing (1) and (2) we get:
$\frac{2}{3}=\frac{T_A{\rho }_B{r}_B}{{\rho }_A{r}_A{T}_B}$
$\frac{r_A}{r_B}=\frac{75\times 3\times 2}{70\times 2\times 5}=\frac{9}{14}$