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NEET Sample Paper NEET Sample Test Paper-68

  • question_answer
    A particle which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as \[\operatorname{F}\left( x \right)=-kx +a{{x}^{3}}.\] Here k and a are positive constants. For \[x\,\,\ge \,\,0\],                               the functional form of the potential energy \[{{U}_{(x)}}\] of the particle is

    A)        

    B)

    C)      

    D) (d)

    Correct Answer: D

    Solution :

    \[F=-\frac{dU}{dx}\,\,\,\Rightarrow \,\,dU=-Fdx\] \[\Rightarrow \,\,\,U=-\int_{0}^{x}{(-kx+a{{x}^{3}})dx}\] \[\therefore \] We get \[U=0\,\,at\,\,x=0\,\,and\,\,x=\sqrt{\frac{2k}{a}}\] Also we get \[U=negative\,\,for\,\,x>\sqrt{\frac{2k}{a}}\] From the given function we can see that \[\operatorname{F} =0\] at \[\operatorname{x}= 0\], i.e., slope of \[U-x\] graph is zero at \[\operatorname{x} =0\].


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