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JEE Main & Advanced Sample Paper JEE Main Sample Paper-27

  • question_answer
    A particle of mass m is executing oscillations about the origin on the X-axis with amplitude A. Its potential energy \[U(x)=a{{x}^{4}}\] where a is positive constant. The x-coordinate of mass where potential energy is one third of the kinetic energy of particle is:

    A)  \[\frac{\pm A}{\sqrt{3}}\]                                 

    B)  \[\frac{\pm A}{\sqrt{2}}\]

    C)  \[\frac{\pm A}{3}\]                              

    D)  \[\frac{\pm A}{2}\]

    Correct Answer: B

    Solution :

    Energy of oscillation \[E=\alpha {{A}^{4}}\] KE of mass \[K=E-U=\alpha ({{A}^{4}}-{{x}^{4}})\] \[\Rightarrow \,K=-3U\] \[\Rightarrow \,\alpha =({{A}^{4}}-{{x}^{4}})=3a{{x}^{4}}\Rightarrow \,\frac{\pm \,A}{\sqrt{2}}\]


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