A) W
B) 2W
C) V21V
D) \[{{4}^{1/3}}\] W
Correct Answer: D
Solution :
From the definition of surface tension (T), the surface tension of a liquid is equal to the work (W) required to increase the surface area of the liquid film by unity at constant temperature. \[\therefore \] \[W=T\times \Delta \,A\] Since, surface area of a sphere is 47iR2 and there are two free surfaces, we have \[W=T\times 8\pi {{R}^{2}}\] ... (i) and volume of sphere \[=\frac{4}{3}\pi {{R}^{3}}\] i.e., \[V=\frac{4}{3}\pi {{R}^{3}}\] \[\Rightarrow \] \[R={{\left( \frac{3V}{4\pi } \right)}^{1/3}}\] ... (ii) From Eqs. (i) and (ii), we get \[W=T\times 8\pi \times {{\left( \frac{3V}{4\pi } \right)}^{2/3}}\]
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