A) \[32\pi {{R}^{2}}T\]
B) \[24\pi {{R}^{2}}T\]
C) \[8\pi {{R}^{2}}T\]
D) \[4\pi {{R}^{2}}T\]
Correct Answer: A
Solution :
The surface tension \[(T)\] of a liquid is equal to the work \[(W)\] required to increase the surface area of the liquid film by unity at constant temperature. As per key idea, tension \[=\frac{work\,\,done}{surface\,\,area}\] or \[T=\frac{W}{\Delta \,\,A}\] Since soap bubble has two surface and surface area of soap bubble is\[4\pi {{R}^{2}}\] where\[R\]is radius of bubble. then \[W=T\times 2\times 4\pi {{R}^{2}}\] Given \[R=2R\] therefore \[W=T\times 2\times 4\pi \times {{(2R)}^{2}}\] \[W=32\pi {{R}^{2}}T\]
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