Question

An open capillary tube is lowered in a vessel with mercury. The difference between the levels of the mercury in the vessel and in the capillary tube $\Delta h=4.6mm.$ What is the radius of curvature of the mercury meniscus in the capillary tube? Surface tension of mercury is $0.46N/m,$ density of mercury is $13.6gm/cc.$

• A. $\frac{1}{340}m$
• B. Information insufficient
• C. $\frac{1}{1020}m$
• D. $\frac{1}{680}m$

Answer 1

The correct option is D $\frac{1}{680}m$

In a capillary tube of radius $r,$ the rise or fall of the level is given by
$\Delta h=\frac{2s\cos \theta }{r\rho g}$
Where $S=$ Surface tension,
$\rho =\text{density of the mercury}$
From figure
$\frac{r}{\cos \theta }=R$
$\Delta h=\frac{2S}{R\rho g}$
$R=\frac{2S}{\Delta h\rho g}$
$=\frac{2\times 0.46}{4.6\times {10}^{-3}\times 13.6\times {10}^3\times 10}$
$\frac{1}{680}m$
Final answer: $\left(b\right)$