Question

The potential energy of a particle excuting shm is 25j when its displacement is half of amplititude the total energy of the particle is?

Answer 1

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)

Answer 2

When the displacement is half of amplitude, its total energy is 10 J.

Explanation:

It is given that, the potential energy of a particle executing SHM is 25 J when its displacement is half of amplitude.

The potential energy of the particle is SHM is given by :

$P=\dfrac{1}{2}m\omega^2x^2$............(1)

x is the displacement in SHM

If x = A/2, P = 2.5 J

The total energy of the particle is SHM is given by :

$T=\dfrac{1}{2}m\omega^2A^2$

So, equation (1) becomes,

$2.5=\dfrac{1}{2}m\omega^2(\dfrac{A}{2})^2$

$10\ J=\dfrac{1}{2}m\omega^2A^2$

$T=10\ J$

So, when the displacement is half of amplitude, its total energy is 10 J.

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