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JEE Main & Advanced Sample Paper JEE Main Sample Paper-11

  • question_answer
    A body is executing simple harmonic motion. At a displacement x from mean position, its potential energy is \[{{E}_{1}}=2J\]and at a displacement y from mean position, its potential energy is \[{{E}_{2}}=8J\]. The potential energy E at a displacement (x + y) from mean position is

    A)  10J                                        

    B)  14J

    C)  18J                                        

    D)  4J

    Correct Answer: C

    Solution :

     \[{{E}_{1}}=\frac{1}{2}k{{x}^{2}},{{E}_{2}}=\frac{1}{2}k{{y}^{2}},\] \[E=\frac{1}{2}k{{(x+y)}^{2}}={{E}_{1}}+{{E}_{2}}+2\sqrt{{{E}_{1}}{{E}_{2}}}\] \[=2+8+2\sqrt{16}=18\,\text{J}\]


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