Class JEE Physics ALL Q #1194
COMPETENCY BASED
APPLY
4 Marks 2026 JEE Main 2026 (Online) 21st January Morning Shift MCQ SINGLE
A potential energy curve U vs x is shown. If $F_{AB}, F_{BC}, F_{CD}, F_{DE}$ are forces in respective regions, arrange magnitudes in decreasing order.
(A) $F_{BC}>F_{AB}>F_{CD}>F_{DE}$
(B) $F_{BC}>F_{AB}>F_{DE}>F_{CD}$
(C) $F_{AB}>F_{BC}>F_{DE}>F_{CD}$
(D) $F_{BC}>F_{DE}>F_{AB}>F_{CD}$
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Step-by-Step Solution

  1. The force is given by the negative gradient of the potential energy: $F = -\frac{dU}{dx}$.
  2. In region AB, the slope is positive and relatively large. Therefore, $F_{AB}$ is negative and has a magnitude proportional to the slope.
  3. In region BC, the potential energy is constant, so the slope is zero. Therefore, $F_{BC} = 0$.
  4. In region CD, the slope is negative and small. Therefore, $F_{CD}$ is positive and has a small magnitude.
  5. In region DE, the slope is positive and has a moderate magnitude. Therefore, $F_{DE}$ is negative and has a moderate magnitude.
  6. Comparing the magnitudes, we have: $|F_{BC}| = 0$, $|F_{AB}|$ is large, $|F_{CD}|$ is small, and $|F_{DE}|$ is moderate.
  7. Therefore, the correct order is $F_{AB} > F_{DE} > F_{CD}$ and $F_{BC}=0$.
  8. Combining these, we get $F_{BC} > F_{AB} > F_{DE} > F_{CD}$ is incorrect. $F_{BC} > F_{AB} > F_{DE} > F_{CD}$ is incorrect. $F_{AB}>F_{BC}>F_{DE}>F_{CD}$ is incorrect. $F_{BC}>F_{DE}>F_{AB}>F_{CD}$ is incorrect.
  9. Since $F_{BC} = 0$, we need to compare the magnitudes of $F_{AB}, F_{DE}, F_{CD}$. From the graph, the magnitude of the slope in region AB is the largest, followed by DE, and then CD. Therefore, $|F_{AB}| > |F_{DE}| > |F_{CD}|$. Since $F_{BC} = 0$, the correct order is $|F_{AB}| > |F_{DE}| > |F_{CD}| > |F_{BC}|$. However, the question asks for the decreasing order of magnitudes, and the options do not include $F_{BC}=0$. The closest option is (C) if we consider the absolute values of the forces. However, since $F_{BC} = 0$, it should be the smallest.
  10. Re-evaluating the slopes: AB has a steep positive slope, BC has zero slope, CD has a shallow negative slope, and DE has a moderate positive slope. Thus, $|F_{AB}|$ is large, $F_{BC} = 0$, $|F_{CD}|$ is small, and $|F_{DE}|$ is moderate. Therefore, the correct order of magnitudes is $|F_{AB}| > |F_{DE}| > |F_{CD}| > |F_{BC}| = 0$. None of the options match this exactly. However, if we consider the closest option, it would be (C), assuming that the question meant to compare the absolute values of the forces.
  11. The correct order should be $F_{AB} > F_{DE} > F_{CD} > F_{BC}$. However, none of the options match this. The closest option is (C), but it has $F_{BC}$ in the middle.
  12. The correct order of magnitudes is $|F_{AB}| > |F_{DE}| > |F_{CD}| > |F_{BC}| = 0$. None of the options are correct.

Correct Answer: None of the options are correct. The correct order should be |F_AB| > |F_DE| > |F_CD| > |F_BC| = 0<\/strong>

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the concept of potential energy and its relation to force (F = -dU/dx) to interpret the given potential energy curve and determine the relative magnitudes of the forces in different regions.
Knowledge Dimension: CONCEPTUAL
Justification: The question requires understanding the relationship between potential energy and force, which is a conceptual understanding rather than recall of facts or execution of a procedure.
Syllabus Audit: In the context of JEE, this is classified as COMPETENCY. The question assesses the student's ability to apply the concepts of potential energy and force to a given scenario, rather than simply recalling definitions or formulas.

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