A) \[\sqrt{\frac{a}{b}}\]
B) \[{{\left( \frac{2a}{b} \right)}^{1/3}}\]
C) \[{{\left( \frac{2a}{b} \right)}^{1/6}}\]
D) \[{{\left( \frac{a}{b} \right)}^{1/3}}\]
Correct Answer: C
Solution :
\[F=0\] and \[U\] is \[-ve\] for stable equilibrium. \[U(x)=\frac{a}{{{x}^{12}}}-\frac{b}{{{x}^{6}}}\] \[F=-\frac{dU}{dx}=-\left[ -12a{{x}^{-13}}+6b{{x}^{-7}} \right]=0\] \[\Rightarrow \,\,12a{{x}^{-13}}=6b{{x}^{-7}}\Rightarrow \,\frac{2a}{b}={{x}^{6}}\] \[\therefore \,\,x={{\left( \frac{2a}{b} \right)}^{1/6}}\]You need to login to perform this action.
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