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A capillary of the shape as shown is dipped in a liquid. Contact angle between the liquid and the capillary is $0^{0}$ and mass of liquid inside the meniscus is to be neglected. $T$ is surface tension of the liquid, $r$ is raidus of the meniscus, $g$ is acceleration due to gravity and $ρ$ is density of the liquid then height $h$ in equilibrium is

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Greater than $\frac{2 T}{r ρ g}$

Equal to $\frac{2 T}{r ρ g}$

Less than $\frac{2 T}{r ρ g}$

of any value depending upon actual values

answer is C.

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Detailed Solution

As weight of liquid in capillary is balanced by surface tension, then $T = 2 π r = π r^{2} h, p g$ (for uniform $r$ radius tube)

$h_{1} = \frac{2 T}{r p g}$

But weight of liquid in tapered tube is more than uniform tube of radius $r$ , then in order to balance is $< h_{1}$

$h_{1} < \frac{2 T}{r p g}$

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