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From a water tap, liquid comes out in from of cylinder. As water moves down, radius of that cylinder decreases. Consider, a very small element of height h and radius R (due to small height radius is assumed to be constant). This element is given in the diagram. An imaginary cross-section ABCD divides this element in two equal semi cylinders. S is surface tension of liquid. Now choose correct statement (s)

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Pressure inside the cylinder is more than atmospheric pressure by $\frac{2 S}{R}$

Surface energy of this elementary cylinder is $S \times 2 π R h$

Force exerted by one half cylinder on another half cylinder due to surface tension is 2Sh

Surface energy of this elementary cylinder is $S [2 π R h + 2 π R^{2}]$

answer is C, D.

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Detailed Solution

Surface energy = free surface are $\times$ surface tension for a cylindrical surface excess pressure is $\frac{S}{R}$ .

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