Two capillary tubes of same diameter are put vertically one each … - Vidyadip

MCQ

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

A
$\frac{10}{9}$
B
$\frac{3}{10}$
C
$\frac{10}{3}$
✓
$\frac{9}{10}$

✓

Answer

Correct option: D.

$\frac{9}{10}$

d
Ascent formula $\mathrm{h}=\frac{2 \mathrm{T} \cos \theta}{\mathrm{rdg}}$

$\Rightarrow \frac{\mathrm{h}_{1}}{\mathrm{h}_{2}}=\frac{\mathrm{T}_{1}}{\mathrm{T}_{2}} \times \frac{\mathrm{d}_{2}}{\mathrm{d}_{1}} \quad[\mathrm{r}, \theta \text { and } \mathrm{g} \text { are constants }]$

$=\frac{60}{50} \times \frac{0.6}{0.8}=\frac{9}{10}$

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