A) \[7.9\times {{10}^{-6}}J\]
B) \[5.92\times {{10}^{-6}}J\]
C) \[2.92\times {{10}^{-6}}J\]
D) \[1.92\times {{10}^{-6}}J\]
Correct Answer: A
Solution :
Let R and r be the radii of big drop and each smaller drop. \[\therefore \] Volume of big drop = volume of smaller drops \[\frac{4}{3}\pi {{R}^{3}}=1000\times \frac{4}{3}\times {{r}^{3}}\] \[\Rightarrow \] \[r=\frac{R}{10}=\frac{0.1\times {{10}^{-2}}}{10}=0.01\times {{10}^{-2}}m\] \[(\therefore R=0.1\times {{10}^{-2}}m\] \[\therefore \] \[r=1\times {{10}^{-4}}m\] The work done in breaking the big drop into 1000 small droplets is \[W=T(1000\times 4\pi {{r}^{2}}-4\pi {{R}^{2}})\] \[=T\times 4\pi (1000\times {{10}^{-8}}-{{10}^{-6}})\] \[=4\pi T\times {{10}^{-6}}(10-1)\] \[=4\pi T\times {{10}^{-6}}\times 9\] \[=36\times 3.14\times 7\times {{10}^{-2}}\times {{10}^{-6}}\] \[=7.9\times {{10}^{-6}}\,\text{J}\]
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