Question

A liquid is contained in a vertical tube of semicircular cross section. The contact angle is zero. The force of surface tension on the curved part and on the flat part are in ratio
(a) 11
(b) 12
(c) π3
(d) 2π

Answer 1

Active Surface Tension Force

Explanation:

Total perimeter of the curved part = semi−circumference of upper area = $\pi \times r$

Total surface tension force = $\pi \times R \times S$

Total perimeter of the flat part =$2 \times R$  

Total surface tension force = $2\times R\times S$

Where, Let the height of the liquid-filled column be L and R be radius

* refer figure for reference

Answer 2

The force of surface tension on the curved part and on the flat part are in ratio is $\pi : 2$.

Explanation:

Formula to calculate surface tension on curved path is as follows.

          F = $S \times \pi \times r$

where,     S = surface tension of the liquid

                r = radius of the tube

Now, formula for surface tension force on flat part is as follows.

          F' = $S \times 2r$

Hence, we will calculate the ratio of surface tension on the curved part and on the flat part as follows.

       $F : F' = S \times \pi \times r : S \times 2r$

                 = $\pi : 2$

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