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
B
15 J
C
10 J
D
12 J

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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