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

  • question_answer
    Assertion             :       In a S.H.M., kinetic and potential energies become equal when the displacement is \[1/\sqrt{2}\] times the amplitude.  Reason                 :       In SHM, kinetic energy is zero when potential energy is maximum.

    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: B

    Solution :

                       In SHM.\[K.E.=\frac{1}{2}m{{\omega }^{2}}({{a}^{2}}-{{y}^{2}})\]and \[P.E.=\frac{1}{2}m{{\omega }^{2}}{{y}^{2}}.\]                            For K.E. = P.E. Þ \[2{{y}^{2}}={{a}^{2}}\] Þ \[y=a/\sqrt{2}.\] Since total energy remains constant through out the motion, which is \[E=K.E.+P.E.\] So, when P.E. is maximum then K.E. is zero and viceversa.


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