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In the figure shown, radii of the limbs (capillary tubes) of a U-tube are $r_{1}$ and $r_{2} (> r_{1})$ . The surface tension of the liquid is T. If the angle of contact is zero, the difference of the heights of the liquid column, h is equal to (Given, $ρ =$ density of liquid)

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$\frac{2 T}{ρg} [\frac{1}{r_{1}} + \frac{1}{r_{2}}]$

$\frac{2 T}{ρg} [\frac{1}{r_{2}} - \frac{1}{r_{1}}]$

$\frac{T}{ρg} [\frac{1}{r_{1}} + \frac{1}{r_{2}}]$

$\frac{T}{ρg} [\frac{1}{r_{1}} - \frac{1}{r_{2}}]$

answer is D.

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Detailed Solution

Pressure at A= Pressure at $A^{'}$

$p_{0} - \frac{2 T}{r_{1}} = (p_{0} - \frac{2 T}{r_{2}}) + hρg$

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