Question

A tube of semicircular cross section contains some liquid and is placed vertically. The angle of contact is zero. The ratio of forces due to surface tension for circular and plane portion of the tube is:

• A. $1:1$
• B. $\pi :2$
• C. $2:\pi$
• D. none of these

Answer 1

The correct option is B $\pi :2$

Let the height of the liquid-filled column be L.

Let the radius be denoted by R.

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

Total surface tension force $=\pi RS$

Total perimeter of the flat part $=2R$

Total surface tension force $=2RS$

Ratio of curved surface force to flat surface force $=\frac{\pi RS}{2RS}=\frac{\pi }{2}$.