Given below are two statements: one is labelled as Assertion $\mathrm{A}$ and the other is labelled as…

Given below are two statements: one is labelled as Assertion $\mathrm{A}$ and the other is labelled as Reason $\mathrm{R}$
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
  1. $\mathrm{A}$ is false but $\mathrm{R}$ is true
  2. Both $\mathrm{A}$ and $\mathrm{R}$ are true but $\mathrm{R}$ is NOT the correct explanation of $\mathrm{A}$
  3. $\mathrm{A}$ is true but $\mathrm{R}$ is false
  4. Both $\mathrm{A}$ and $\mathrm{R}$ are true and $\mathrm{R}$ is the correct explanation of $\mathrm{A}$

Solution

Assertion is correct as central forces are conservative in nature, i.e. work done is independent of path.
Reason is true as some forces in mechanics like, friction are non-conservative because work done depends on path and only conservative forces have an associated potential energy.
Also, reason does not explain assertion.

Asked in: JEE Main 2025 (28 Jan Shift 1)

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