The variation of potential energy (V) with distance (x) for a particle is shown in the graph. Rank the various regions AB, BC, CD and DE in decreasing order of the magnitude of force acting on the particle

Options:

1. F({BC}) > F({CD}) > F({DE}) > F({AB})
2. F({CD}) > F({AB}) > F({BC}) > F({DE})
3. F({CD}) > F({DE}) > F({AB}) > F({BC})
4. F({BC}) > F({AB}) > F({DE}) > F({CD})

Solution:

Force is given by $[ F = -\frac{dV}{dx} ]$ Magnitude of force depends on slope of V–x graph. Comparing slopes:

• BC → maximum slope
• AB → next
• DE → smaller
• CD → least

$[ F_{BC} > F_{AB} > F_{DE} > F_{CD} ]$ ✅ Correct Answer: (4)

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