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.

• A. \( F_{CD}>F_{AB}>F_{BC}>F_{DE} \)
• B. \( F_{CD}>F_{DE}>F_{AB}>F_{BC} \)
• C. \( F_{BC}>F_{AB}>F_{DE}>F_{CD} \)
• D. \( F_{BC}>F_{CD}>F_{DE}>F_{AB} \)

Hint:

Remember that the force is related to the \textbf{slope} of the potential energy graph, not the value of the potential energy itself. A steeper slope (either positive or negative) means a larger force magnitude. A horizontal line (zero slope) means zero force.

Answer 1

The Correct Option is C

To rank the magnitudes of force acting on the particle in different regions, we use the relation between force and potential energy.

\[ F = -\frac{dV}{dx} \]

Thus, the magnitude of the force depends on the slope of the potential energy curve. A steeper slope corresponds to a larger force magnitude, while a horizontal segment implies zero force. 

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Analysis of each segment:

• Segment AB: Positive slope → force is negative with a moderate magnitude.
• Segment BC: Steeper positive slope than AB → force is negative with the largest magnitude.
• Segment CD: Horizontal segment (zero slope) → force magnitude is zero.
• Segment DE: Negative slope → force is positive, but the slope is less steep than BC, so the force magnitude is smaller than BC but greater than CD.

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Ranking of force magnitudes (highest to lowest):

\[ F_{BC} > F_{AB} > F_{DE} > F_{CD} \]

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Final Answer:

\(\boxed{F_{BC} > F_{AB} > F_{DE} > F_{CD}}\)