Question

A capillary tube made of glass of radius $0.15\, mm$ is dipped vertically in a beaker filled with methylene iodide (surface tension $=0.05 \,Nm ^{-1}$ density $=667\, kg m ^{-3}$ ) which rises to height $h$ in the tube. It is observed that the two tangents drawn from liquid-glass interfaces (from opp. sides of the capillary) make an angle of $60^{\circ}$ with one another. Then $h$ is close to $\left( g = \,10 \,ms ^{-2}\right)$

• A. $0.137\, m$
• B. $0.172\, m$
• C. $0.087\, m$
• D. $0.049\, m$

Answer 1

Answer: (C)

$r \rightarrow$ radius of capillary
$R \rightarrow$ Radius of meniscus.
From figure, $\frac{r}{R}=\cos 30^{\circ}$
$R =\frac{2 r }{\sqrt{3}}=\frac{2 \times 0.15 \times 10^{-3}}{\sqrt{3}} $
$=\frac{0.3}{\sqrt{3}} \times 10^{-3} m$
Height of capillary
$h =\frac{2 T }{\rho gR }=2 \sqrt{3} T$
$h =\frac{2 \times 0.05}{667 \times 10 \times\left(\frac{0.3 \times 10^{-3}}{\sqrt{3}}\right)} $
$h =0.087 m$