Question

A liquid is filled into a tube with semi elliptical cross section as shown in the figure. The ratio of the surface tension forces on the curved part and the plane part of the tube in vertical position will be:

• A. $\frac{\pi (a+b)}{4b}$
• B. $\frac{2\pi a}{b}$
• C. $\frac{\pi a}{4b}$
• D. $\frac{\pi (a-b)}{4b}$

Answer 1

The correct option is A $\frac{\pi (a+b)}{4b}$

From the figure,

Curved part = Semi perimeter = \dfrac{\pi(a+b)}{2}$

and the plane part = minor axis = $2b$

Force on curved part = $T\times \frac{\pi (a+b)}{2}$

and force on plane part $=T\times 2b$

Therefore,

Ratio $=\frac{\pi (a+b)}{4b}$