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 \(\left.=667\, kg m ^{-3}\right)\) 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 \(......m\) \(\left(g=10\, ms ^{-2}\right)\)

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Answer & Solution

Correct Answer

(C) \(0.087\)

Detailed explanation

\(r \rightarrow\) 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

\(h =\frac{2 T }{\rho gR }=2 \sqrt{3} T\)

\(h =\frac{2 \times 0.05}{667 \times 10 \times\left(\frac{0.3 \times 10^{-3}}{\sqrt{3}}\right)}\)

\(h=0.087 m\)

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