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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 beA. zeroB. `M^(2)//4N`C. `N^(2)//4M`D. `MN^(2)//4` |
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Answer» 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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