Potential energy ( $V$ ) versus distance ( $x$ ) is given by the graph. Rank various regions as per

Question

Potential energy ( $V$ ) versus distance ( $x$ ) is given by the graph. Rank various regions as per the magnitudes of the force ( F ) acting on a particle from high to low.

Professor PC Thomas Classes · Answer

The magnitude of the force acting on the particle is given by the magnitude of the slope of the potential energy versus distance graph, $|F| = \left| -\frac{dV}{dx} ight|$. For region AB, slope is $1 	ext{ V/m} \Rightarrow F_{AB} = 1$. For region BC, slope is $3 	ext{ V/m} \Rightarrow F_{BC} = 3$. For region CD, slope is $0 \Rightarrow F_{CD} = 0$. For region DE, slope is $-0.5 	ext{ V/m} \Rightarrow F_{DE} = 0.5$. Therefore, the order of force magnitude is $F_{BC} > F_{AB} > F_{DE} > F_{CD}$.