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  4. On a particle placed at origin a variable force F=-a x (where a is a positive constant) is applied. If U(0)=0, the graph between potential energy of particle U(x) and x is best represented by

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Q. On a particle placed at origin a variable force $F=-a x$ (where $a$ is a positive constant) is applied. If $U(0)=0$, the graph between potential energy of particle $U(x)$ and $x$ is best represented by

Work, Energy and Power

Solution:

$F=-a x=\frac{-d U}{d x}$
Integrating both sides
$U=\frac{a x^{2}}{2}$

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