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in Physics by (54.5k points)

It is said that a liquid rises or is depressed in a capillary due to the surface tension. If a liquid neither rises nor depresses in a capillary, can we conclude that the surface tension of the liquid is zero?

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No. 

Because the rise of a liquid in a capillary tube depends on other factors also as we can see in the expression for height h, h = 2S*cosθ/(rρg) 

The rise h depends on S, θ, r and ρ. Since it is a capillary tube, r is small and it can not make h zero. Even the density of a liquid ρ will not be so high to make h zero. But the cosθ can be zero for θ =90°, thus making the rise h =0.   

So if a liquid neither rises nor depresses in a capillary we can not conclude that the surface tension of the liquid is zero. The angle of contact between the liquid and the wall of the tube may be about 90°.

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