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  • Answer please! The potential energy of a particle executing SHM is 2.5 J, when its displacement is half of the amplitude. The total energy of the particle is

The potential energy of a particle executing SHM is 2.5 J, when its displacement is half of the amplitude. The total energy of the particle is

  • Option 1)

    18 J

  • Option 2)

    10 J

  • Option 3)

    12 J

  • Option 4)

    2.5 J

 

Answers (1)

best_answer

\frac{Potential\;Energy \;(U)}{Total\;Energy\;(E)} = \frac{^{1}/_{2}\cdot m\omega^{2}y^{2}}{^{1}/_{2}\cdot m\omega^{2}a^{2}} = \frac{y^{2}}{a^{2}}

So, \frac{2.5}{E} = \frac{(\frac{a}{2})^{2}}{a^{2}} \Rightarrow E = 10\; J

 

Kinetic energy in S.H.M. -

K.E.= \frac{1}{2}mu^{2}\\ \: \: \: = \frac{1}{2}m\left ( A^{2} -x^{2}\right )\omega ^{2}

 

- wherein

K.E.= \frac{1}{2}K\left ( A^{2}-x^{2} \right ) \\K= m\omega ^{2}

 

 

 


Option 1)

18 J

This is incorrect.

Option 2)

10 J

This is correct.

Option 3)

12 J

This is incorrect.

Option 4)

2.5 J

This is incorrect.

Posted by

Avinash

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