A) \[2.0\times {{10}^{-6}}J\]
B) \[2.7\times {{10}^{-6}}J\]
C) \[4\times {{10}^{-6}}J\]
D) \[5.4\times {{10}^{-6}}J\]
Correct Answer: B
Solution :
\[\frac{4}{3}\pi {{R}^{3}}=64\times \frac{4}{3}\pi {{r}^{3}}\] Or \[r=\frac{R}{4}=\frac{{{10}^{-3}}}{4}\] Hence, work done \[W=T\times (64\times 4\pi {{r}^{2}}-4\pi {{R}^{2}})\] \[W=72\times {{10}^{-3}}\times 4\pi \left[ 64\times {{\left( \frac{{{10}^{-3}}}{4} \right)}^{2}}-{{({{10}^{-3}})}^{2}} \right]\] \[W=2.7\times {{10}^{-6}}J\]
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