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