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

Answer 1

Answer: (A)

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

Answer 2

From the figure Curved part = semi perimeter $= \frac { \pi ( a + b ) } { 2 }$

and the plane part = minor axis = 2b

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

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

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