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Mechanical Properties of Fluids

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Question : 18 of 31
Marks: +1, -0
Figure (a) shows a thin liquid film supporting a small weight =4.5×102N= 4.5 \times 10^{-2} \, \text{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.
Solution:  
(a) Here, length of the film supporting the weight l=40cm=0.4ml = 40 \, \text{cm} = 0.4 \, \text{m}
Total weight supported (i.e. force)=4.5×102N= 4.5 \times 10^{-2} \, \text{N}.
Film has two free surfaces,
\therefore Surface tension, T=4.5×1022×0.4T = \frac{4.5 \times 10^{-2}}{2 \times 0.4}
=5.625×102Nm1= 5.625 \times 10^{-2} \, \text{Nm}^{-1}.
Since the liquid is same for all the cases (a), (b) and (c), and temperature is also same, therefore surface tension for cases (b) and (c) will also be the same =5.625×102= 5.625 \times 10^{-2}. In figure (b), and (c), the length of the film supporting the weight is also the same as that of (a), hence the total weight supported in each case is 4.5×102N4.5 \times 10^{-2} \, \text{N}.
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