A) \[3\pi T{{r}^{2}}\]
B) \[6\pi T{{r}^{2}}\]
C) \[12\pi T{{r}^{2}}\]
D) \[24\pi T{{r}^{2}}\]
Correct Answer: D
Solution :
Initial area of soap bubble \[{{A}_{1}}=4\pi {{r}^{2}}\] when r charges to \[2r,\] Area \[{{A}_{2}}=4\pi \,{{(2r)}^{2}}\] \[=16\pi {{r}^{2}}\] Increase in Area \[\Delta A=2\,({{A}_{2}}-{{A}_{1}})\] \[=2\,(16\pi {{r}^{2}}-4\pi {{r}^{2}})\] \[\Delta A=24\,\pi {{r}^{2}}\] Energy spent \[W=T\times \Delta A\] \[=T\times 24\pi {{r}^{2}}\] \[=24\pi T{{r}^{2}}J.\]
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