question_answer 18)

Fig. 9(a) below shows a thin film supporting a small weight \[\text{Strain=}\frac{\text{stress}}{\text{modulusnofelasticity}}\text{=}\frac{\text{F/A}}{\text{G}}\] What is the weight supported by a film of the same liquid at the same temperature in Fig 7(NCT). 9 (b) and (c)? Explain your answer physically.

Answer:

(a) Here, length of the film supporting the weight \[=40\,cm=0.4\,m\]. Total weight supported (or force)\[=\frac{F}{AG}\] Film has two free surfaces, \[\therefore \] Surface tension, \[=\frac{44500}{\left( 15\cdot 2\times 19\cdot 2\times {{10}^{-6}} \right)\times 42\times {{10}^{9}}}=3\cdot 65\times {{10}^{-3}}\] 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\[1\cdot 5\]. In Fig. 7(b). 38(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 \[{{10}^{8}}N{{m}^{-2}},\]