Question

A square wire frame of size $L$ is dipped in a liquid. On taking out a membrane is formed. If the surface tension of liquid is $T$, then force acting on the frame will be

• A. $2TL$
• B. $4TL$
• C. $8TL$
• D. $16TL$

Answer 1

The correct option is C $8TL$

Surface tension makes fluid films minimize their surface areas. Since the square frame is a closed polygon, the net vector force acting on it due to the fluid film will be zero, but this force will pull on the frame and try to collapse it. This force has thus got a nature to try to deform the frame. So we need to find what this total deforming force is.

Since a membrane has two sides, there will be two pulling forces on each arm of the frame, one due to each of the sides. Now, the pulling force due to surface tension of one side of the film is given by $TL$.

Since the frame has 4 arms and each arm is pulled by two sides of the membrane, the total deforming force is $8TL$.