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Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: In a central force field, the work done is independent of the path chosen. Reason R: Every force encountered in mechanics does not have an associated potential energy. In the light of the above statements, choose the most appropriate answer from the options given below

Asked in JEE Main 28th Jan 1st Shift 2025 · Potential energy functions and force

• (1) Both A and R are true but R is not the correct explanation of A
• (2) A is true but R is false
• (3) A is false but R is true
• (4) Both A and R are true and R is the correct explanation of A

Step-by-step solution

Why the other options are wrong

• (2) Comes from thinking every mechanical force has a potential; friction does not.
• (3) Comes from thinking a central force can be path dependent; a force depending only on r is conservative.
• (4) Comes from accepting R as the reason; the existence of non-conservative forces says nothing about central ones.

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