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JEE Main & Advanced Physics Wave Mechanics Question Bank Self Evaluation Test - Oscillations

  • question_answer
    The angular velocity and the amplitude of a simple pendulum is o and a respectively. At a displacement x from the mean position if its kinetic energy is T and potential energy is V, then the ratio of T to Vis

    A) \[\frac{({{a}^{2}}-{{x}^{2}}{{\omega }^{2}})}{{{x}^{2}}{{\omega }^{2}}}\]

    B) \[\frac{{{x}^{2}}{{\omega }^{2}}}{({{a}^{2}}-{{x}^{2}}{{\omega }^{2}})}\]

    C) \[\frac{({{a}^{2}}-{{x}^{2}})}{{{x}^{2}}}\]   

    D) \[\frac{{{x}^{2}}}{({{a}^{2}}-{{x}^{2}})}\]

    Correct Answer: C

    Solution :

    [c] \[P.E.,\,\,\,V=\frac{1}{2}m{{\omega }^{2}}{{x}^{2}}\] and \[K.E.,\,\,T=\frac{1}{2}m{{\omega }^{2}}({{a}^{2}}-{{x}^{2}})\]      \[\therefore \,\,\frac{T}{V}=\frac{{{a}^{2}}-{{x}^{2}}}{{{x}^{2}}}\]


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