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 :
Key Idea: 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, \[\text{tension=}\frac{\text{work done}}{\text{Surface area}}\] or \[T=\frac{W}{\Delta \,A}\] Since, soap bubble has two surfaces 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 \[W=T\times 2\times 4\pi \,{{\left( 2R \right)}^{2}}\] \[W=32\pi \,{{R}^{2}}\,T\]
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