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JEE Main & Advanced Physics Simple Harmonic Motion Question Bank Mock Test - Simple Harmonic Motion

  • question_answer
    A body is executing Simple Harmonic Motion. At a displacement \[x\] its potential energy is \[{{E}_{1}}\] and at a displacement \[y\] its potential energy is \[{{E}_{2}}\] The potential energy \[E\] at displacement \[(x+y)\]is

    A) \[\sqrt{E}=\sqrt{{{E}_{1}}}-\sqrt{{{E}_{2}}}\]

    B) \[\sqrt{E}=\sqrt{{{E}_{1}}}+\sqrt{{{E}_{2}}}\]

    C) \[E={{E}_{1}}+{{E}_{2}}\]   

    D) \[E={{E}_{1}}-{{E}_{2}}\]

    Correct Answer: B

    Solution :

    [b] \[{{E}_{1}}=\frac{1}{2}K{{x}^{2}}\Rightarrow x=\sqrt{\frac{2{{E}_{1}}}{K}},{{E}_{2}}=\frac{1}{2}K{{y}^{2}}\] \[\Rightarrow y=\sqrt{\frac{2{{E}_{2}}}{K}}\]  And \[E=\frac{1}{2}K{{(x+y)}^{2}}\Rightarrow x+y=\sqrt{\frac{2E}{K}}\] \[\Rightarrow \sqrt{\frac{2{{E}_{1}}}{K}}+\sqrt{\frac{2{{E}_{2}}}{K}}=\sqrt{\frac{2E}{K}}\Rightarrow \sqrt{{{E}_{1}}}+\sqrt{{{E}_{2}}}=\sqrt{E}\]


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