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Question

The potential energy of a particle executing  $$S.H.M$$ is $$2.5 J$$.
When its displacement is half of amplitude the total energy of the particle  be


A
18 J
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B
15 J
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C
10 J
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D
12 J
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Solution

The correct option is C 10 J
$$\begin{array}{l} We\, \, know, \\ \dfrac { { potential\, \, energy\, \left( U \right)  } }{ { Total\, \, energy\left( E \right)  } } =\dfrac { { \dfrac { 1 }{ 2 } m{ \omega ^{ 2 } }{ y^{ 2 } } } }{ { \dfrac { 1 }{ 2 } m{ \omega ^{ 2 } }{ a^{ 2 } } } } =\dfrac { { { y^{ 2 } } } }{ { { a^{ 2 } } } }  \\ So, \\ \dfrac { { 2.5 } }{ E } =\dfrac { { { { \left( { \dfrac { a }{ 2 }  } \right)  }^{ 2 } } } }{ { { a^{ 2 } } } }  \\ E=10\, \, J \end{array}$$

Physics

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