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(C) The relationship between force $F$ and potential energy $U$ is given by $F = -\frac{dU}{dx}$.$1$. For $0 < x < a$,the graph of $U(x)$ is a straigh

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(C) The relationship between force $F$ and potential energy $U$ is given by $F = -\frac{dU}{dx}$.$1$. For $0  0)$. Thus,$U(x) = kx$. The force is $F = -\frac{d}{dx}(kx) = -k$. This is a negative constant value.$2$. For $x > a$,the graph of $U(x)$ is a horizontal line,meaning $U(x)$ is constant. Thus,$\frac{dU}{dx} = 0$,which implies $F = 0$.Comparing this with the given options,the graph that shows a negative constant force for $0  a$ is Graph $C$.

The potential energy $U(x)$ of a particle is shown in the figure. Which of the following graphs represents the force $F(x)$ acting on it?

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