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) 1:1
(b) 1:2
(c) π:3
(d) 2:π

Answer 1

Correct option: (c)


Let the height of the liquid-filled column be L.
Let the radius be denoted by R.

$$\begin{gathered} \mathrm{Total}\mathrm{perimeter}\mathrm{of}\mathrm{the}\mathrm{curved}\mathrm{part}=\mathrm{semi}-\mathrm{circumference}\mathrm{of}\mathrm{upper}\mathrm{area}=\mathrm{\pi r} \\ \mathrm{Total}\mathrm{surface}\mathrm{tension}\mathrm{force}=\pi RS \\ \mathrm{Total}\mathrm{perimeter}\mathrm{of}\mathrm{the}\mathrm{flat}\mathrm{part}=2R \\ \mathrm{Total}\mathrm{surface}\mathrm{tension}\mathrm{force}=2RS \\ \mathrm{Ratio}\mathrm{of}\mathrm{curved}\mathrm{surface}\mathrm{force}\mathrm{to}\mathrm{flat}\mathrm{surface}\mathrm{force}=\frac{\mathit{\pi }\mathit{R}\mathit{S}}{\mathit{2}\mathit{R}\mathit{S}}=\frac{\mathrm{\pi }}{2} \end{gathered}$$