Question

Figure (a) shows a thin liquid film supporting a small weight = 4.5 × 10⁻² N. What is the weight supported by a film of the same liquid at the same temperature in figure (b) and (c)? Explain your answer physically.

Answer 1

As we know that

Surface tension is given by force per unit length i.e.

Surface tension=Force/Length

In case of thin film since there are actually two surfaces acting i.e. one which you can see in diagram and the other which is behind the diagram right opposite to the one which is visible , thus the

Surface tension = Force/(2*length)

here we see that surface tension depends on force  and length along which the force acts ..

here we see that the length is same for all the diagrams and even the liquid and temperature is also same and hence inorder to support a weight .. it should support the same weight as in figure a inorder to be balanced

Answer 2

First , we take case (a):

The length of the liquid film supported by the weight, l = 40 cm = 0.4 cm

The weight supported by the film, W = 4.5 × 10–2 N

So , A liquid film has 2 free surfaces .

∴ Surface tension = W / 2l

= 4.5 × 10-2 / (2 × 0.4)  = 5.625 × 10-2 N/m

In all the three figures, the liquid is the same. Temperature is also the same for each case. Hence, the surface tension in figure (b) and figure (c) is the same as in figure (a), that is , 5.625 × 10–2 N m–1.

Since the length of the film in all the cases is 40 cm, the weight supported in each case is 4.5 × 10–2 N.