A) \[32\pi {{R}^{2}}T\]
B) \[24\pi {{R}^{2}}T\]
C) \[16\pi {{R}^{2}}T\]
D) \[8\pi {{R}^{2}}T\]
Correct Answer: B
Solution :
Energy needed to double the radius \[E=T.2\Delta A\] \[=T.2\left\{ 4\pi r_{2}^{2}-4\pi r_{1}^{2} \right\}\] \[=T.2\times 4\pi \{r_{2}^{2}-r_{1}^{2}\}\] \[=T.2\times 4\pi \{{{(2R)}^{2}}-{{(R)}^{2}}\}\] \[=8\pi T.\{4{{R}^{2}}-{{R}^{2}}\}\] \[=24\pi {{R}^{2}}T\]
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