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
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
- (A) is true but is false
- (B)Both and are true but is NOT the correct explanation of ✓ Correct
- (C)Both and are true and is the correct explanation of
- (D) is false but is true
Answer: (B)
Solution
A central force is directed always toward (or away from) a fixed center and depends only on the distance from that center; such forces are conservative, so the work done in moving between two points is independent of the path taken. Assertion A is true.
Reason R states that not every force encountered in mechanics has an associated potential energy — true in general, since non-conservative forces such as friction have none — but this general fact about some forces lacking a potential energy does not explain why central forces in particular are path-independent; that instead follows from the radial, distance-dependent nature of central forces. So Reason R, though a true statement, is not the correct explanation of Assertion A.
Reason R states that not every force encountered in mechanics has an associated potential energy — true in general, since non-conservative forces such as friction have none — but this general fact about some forces lacking a potential energy does not explain why central forces in particular are path-independent; that instead follows from the radial, distance-dependent nature of central forces. So Reason R, though a true statement, is not the correct explanation of Assertion A.
JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Single correct option