A) \[W/2\]
B) \[\sqrt{2}\,W\]
C) \[^{3}\sqrt{2}\,W\]
D) \[^{3}\sqrt{4}\,W\]
Correct Answer: D
Solution :
Work done to form a soap bubble \[W=8\pi {{R}^{2}}T\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(As\,\,V\propto {{R}^{3}}\,\,\,\,\therefore \,\,R\propto {{V}^{1/3}})\]\[\therefore \,\,\,\,\,\,\,W\propto {{V}^{2/3}}\] \[\frac{{{W}_{2}}}{{{W}_{1}}}\,\,=\,\,{{\left( \frac{{{V}_{2}}}{{{V}_{1}}} \right)}^{2/3}}\,=\,\,{{(2)}^{2/3}}\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,{{W}_{2}}\,\,=\,\,{{(4)}^{1/3}}\,W\]
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