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MCQEasyJEE 2026Potential Energy & Conservative Forces

JEE Physics 2026 Question with Solution

Given below are two statements:

Statement I: An object moves from position r⃗1\vec{r}_1 to position r⃗2\vec{r}_2 under a conservative force field F⃗\vec{F}. The work done by the force is W=−∫r⃗1r⃗2F⃗⋅dr⃗.W = -\int_{\vec{r}_1}^{\vec{r}_2} \vec{F} \cdot d\vec{r}.

Statement II: Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force.

In the light of the above statements, choose the correct answer from the options given below:

  • A

    Statement I is true but Statement II is false

  • B

    Statement I is false but Statement II is true

  • C

    Both Statement I and Statement II are true

  • D

    Both Statement I and Statement II are false

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: Two statements about work done by a conservative force.

Find: Which statement is true.

Step 1: Analyze Statement I. For a conservative force field, the work done in moving a particle from position r⃗1\vec{r}_1 to r⃗2\vec{r}_2 is given by

W=−∫r⃗1r⃗2F⃗⋅dr⃗W = -\int_{\vec{r}_1}^{\vec{r}_2} \vec{F} \cdot d\vec{r}

This correctly represents the work done by a conservative force as written in the solution. Therefore, Statement I is true.

Step 2: Analyze Statement II. A particle may move between two points along infinitely many paths, but for a conservative force the work done depends only on the initial and final positions, not on the path. Therefore, the claim that the work done changes with the path is incorrect. Hence, Statement II is false.

Conclusion: Statement I is true but Statement II is false. The correct option is A.

Concept-Based Explanation

Given: The force field is conservative.

Find: Whether each statement is correct.

For a conservative force, the important property is path independence. This means that if a particle moves from one point to another, the work done by the conservative force remains the same for all possible paths between those two points.

So, even though infinitely many paths may exist, the work done does not vary with the chosen path.

Thus:

  • Statement I is true.
  • Statement II is false.

Therefore, the correct option is A.

Common mistakes

  • Students often think that because many different paths are possible, the work done must also be different. This is wrong for a conservative force because work depends only on the initial and final positions. Always check whether the force is conservative before deciding path dependence.

  • A common mistake is confusing conservative and non-conservative forces. For non-conservative forces such as friction, work can depend on the path, but for conservative forces it does not. Use the defining property of the force type before drawing the conclusion.

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