Question

A capillary tube made of glass of radius $0.15mm$ is dipped vertically in a beaker filled with methylene iodide (surface tension $=0.05N{m}^{-1}$ density $=667kg{m}^{-3}$ ) 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 $\left(g=10m{s}^{-2}\right)$

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

Answer 1

Answer: (C)

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