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Ankita Malhotra
Asked: 2022-11-07T09:05:22+05:30 In:

If the potential energy of a gas molecule is `U=(M)/(r^(6))-(N)/(r^(12)),M ` and `N` being positive constants, then the potential energy at equlibrium must be
A. zero
B. `M^(2)//4N`
C. `N^(2)//4M`
D. `MN^(2)//4`

If the potential energy of a gas molecule is `U=(M)/(r^(6))-(N)/(r^(12)),M ` and `N` being positive constants, then the potential energy at equlibrium must be
A. zero
B. `M^(2)//4N`
C. `N^(2)//4M`
D. `MN^(2)//4`
Parabola
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1 Answer

  1. Correct Answer – B
    Here, `U=(M)/(r^(6))-(N)/(r^(12)),`
    `F=-(dU)/(dr)=(-d)/(dr)((M)/(r^(6))-(N)/(r^(12)))`
    `=((-6M)/(r^(7))-(12N)/(r^(13)))`
    In equilibrium position, `F=0`
    `:. (6M)/(r^(7))=(12N)/(r^(13))` or ` r^(6)=(2N)/(r^(13))`
    Hence, `U=(M)/((2N//M))-(N)/((2N//M)^(2))=(M^(2))/(4N)`

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