JEE Main & Advanced Physics Work, Energy, Power & Collision Question Bank Work Done by Variable Force

  • question_answer
    The potential energy between two atoms in a molecule is given by \[U(x)=\frac{a}{{{x}^{12}}}-\frac{b}{{{x}^{6}}}\]; where a and b are positive constants and x is the distance between the atoms. The atom is in stable equilibrium when               [CBSE PMT 1995]

    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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