JEE Main & Advanced Physics Simple Harmonic Motion Question Bank Assertion and Reason

  • question_answer
    Assertion             :       The graph between velocity and displacement for a harmonic oscillator is a parabola.  Reason                 :       Velocity does not change uniformly with displacement in harmonic motion.

    A)             If both assertion and reason are true and the reason is the correct explanation of the assertion.

    B)             If both assertion and reason are true but reason is not the correct explanation of the assertion.

    C)             If assertion is true but reason is false.

    D)             If the assertion and reason both are false.

    E)             If assertion is false but reason is true.

    Correct Answer: E

    Solution :

                       In SHM, \[v=\omega \sqrt{{{a}^{2}}-{{y}^{2}}}\] or \[{{v}^{2}}={{\omega }^{2}}{{a}^{2}}-{{\omega }^{2}}{{y}^{2}}.\] Dividing both sides by \[{{\omega }^{2}}{{a}^{2}},\ \frac{{{\nu }^{2}}}{{{\omega }^{2}}{{a}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}}=1.\] This is the equation of an ellipse. Hence the graph between v and y is an ellipse not a parabola.


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