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

Solution

Physics sir · 4 steps

Judge A and R separately first, then ask whether R actually explains why A is true.

1. Check Assertion A. A central force points along the line to a fixed centre, and its size depends only on the distance r: F⃗ = f(r) r. Only the radial part of any displacement does work, so W = ∫_(r₁)^(r₂) f(r) dr. This depends only on the start and end distances, so the force is conservative and A is true.
2. Check Reason R. Friction and air drag are forces met in mechanics, but the work they do depends on the path taken. No potential energy function can be defined for them, so R is true.
3. Does R explain A. A is true because a central force depends only on r and has a potential energy U(r). R talks about other forces that have no potential energy at all. It says nothing about why a central force is path independent, so R is not the explanation of A.
4. So. Both statements are true, but R does not explain A. The answer is (b).

The idea to keep. Path-independent work means the force is conservative and has a potential energy. Central forces like gravity and the electric force between charges qualify. Friction and drag do not.

Answer from the NTA final answer key. Solution by PrepWiser.