Figure $(a)$ shows a thin liquid film supporting a small weight $= 4.5 \times 10^{-2} \, N$. 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.

(A) Consider case $(a)$:
The length of the liquid film supported by the weight is $l = 40 \, cm = 0.4 \, m$.
The weight supported by the film is $W = 4.5 \times 10^{-2} \, N$.
$A$ liquid film has two free surfaces. Therefore,the force due to surface tension $(S)$ acts along both surfaces.
Surface tension $S = \frac{W}{2l} = \frac{4.5 \times 10^{-2}}{2 \times 0.4} = 5.625 \times 10^{-2} \, N \, m^{-1}$.
In all three figures,the liquid is the same and the temperature is constant. Hence,the surface tension remains the same for all cases.
Since the length of the film $(l = 0.4 \, m)$ is the same in all cases,the force supported by the film,which is $W = 2Sl$,remains constant.
Therefore,the weight supported in each case $(b)$ and $(c)$ is $4.5 \times 10^{-2} \, N$.