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 $T$, force acting on the frame will be

• A. 2$TL$
• B. 4$TL$
• C. 8$TL$
• D. 10$TL$

Answer 1

Answer: (C)

8$TL$

Answer 2

When a square wire frame of side $L$ is dipped in a liquid and taken out, a liquid film is formed across the frame. A liquid film has two free surfaces.
The surface tension $T$ is the force per unit length acting tangentially to the surface.
The liquid film is in contact with the wire frame along its perimeter.
The perimeter of the square frame is $P = 4L$.
Since there are two surfaces of the liquid film (one on each side), the total length along which the surface tension acts on the frame is twice the perimeter.
Total length $= 2 \times P = 2 \times (4L) = 8L$.
The force acting on the frame due to surface tension is given by the product of the surface tension and the total length of contact.
Force $F = T \times (\text{Total length of contact})$
$F = T \times (8L) = 8TL$.
This force acts inwards, trying to contract the film and pull the frame.