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Law of Conservation of Mechanical Energy

Potential ene...

Question

Potential energy of a particle is given by $U = x^{2} - 6 x + 29$ . Locate the position where the particle is in stable equilibrium.

x = 2

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x = 4

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x = 3

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x = 9

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Solution

The correct option is C $x = 3$
$U = x^{2} - 6 x + 29$
$= x^{2} - 6 x + 9 + 20$
$= (x - 3)^{2} + 20$
$\Rightarrow U \geq 20$ and $U_{min} = 20$ at $x = 3$
$U$ is minimum(stable equilibrium) at $x = 3$

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