A glass capillary tube is of the shape of a truncated cone with an apex angle $α$ so that its two ends have cross section of different radii. When dipped in water vertically, the water rises in it to a height h, where the radius of its cross-section is b if the surface tension of water is S, its density is $ρ$ , and contact angle with glass is $θ$ when value of h will be (g is the acceleration due to gravity) $h = \frac{kS}{3 ρgb} \cos (θ + \frac{α}{2})$ then k is

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answer is 6.

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Detailed Solution

$Let r = radius of curvature of meniscus \Rightarrow b = rcos (θ + \frac{α}{2}) \Rightarrow r = \frac{b}{\cos (θ + \frac{α}{2})}$

Now, the excess pressure is equal to pressure due to height of water.

$hρg = \frac{2 S}{r} \Rightarrow h = \frac{2 S}{ρgb} \cos (θ + \frac{α}{2})$

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