First slide

Surface tension and surface energy

Question

Two capillary tubes of same diameter are put vertically one each in two liquids whose relative densities are 0.8 and 0.6 and surface tensions are 60 and 50 dyne/cm respectively Ratio of heights of liquids in the two tubes $\frac{h_{1}}{h_{2}}$ is

Moderate

A

$\frac{10}{9}$
B

$\frac{3}{10}$
C

$\frac{10}{3}$
D

$\frac{9}{10}$

Solution

$Ascent formula h = \frac{2 Tcos θ}{rdg}$
$\begin{array}{l} \Rightarrow \frac{h_{1}}{h_{2}} = \frac{T_{1}}{T_{2}} \times \frac{d_{2}}{d_{1}} (r, θ and g are constants) \\ = \frac{60}{50} \times \frac{0 .6}{0 .8} = \frac{9}{10} \end{array}$

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