A) \[x=\sqrt[6]{\frac{11a}{5b}}\]
B) \[x=\sqrt[6]{\frac{a}{2b}}\]
C) \[x=0\]
D) \[x=\sqrt[6]{\frac{2a}{b}}\]
Correct Answer: D
Solution :
Condition for stable equilibrium \[F=-\frac{dU}{dx}=0\] Þ \[-\frac{d}{dx}\left[ \frac{a}{{{x}^{12}}}-\frac{b}{{{x}^{6}}} \right]=0\] Þ \[-12a{{x}^{-13}}+6b{{x}^{-7}}=0\] Þ \[\frac{12a}{{{x}^{13}}}=\frac{6b}{{{x}^{7}}}\]Þ \[\frac{2a}{b}={{x}^{6}}\]Þ \[x=\sqrt[6]{\frac{2a}{b}}\]
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