Question

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.

• A. A is true but R is false
• B. Both A and R are true and R is the correct explanation of A
• C. Both A and R are true but R is NOT the correct explanation of A
• D. A is false but R is true

Hint:

Distinguish between conservative and non-conservative forces when discussing work and energy: conservative forces have path-independent work and associated potential energy.

Answer 1

The Correct Option is C

Statement A is true because in a central force field (like gravitational or electrostatic), forces are conservative and hence work done is path independent. Statement R is true in the sense that not all forces (like friction) have potential energy; however, it does not correctly explain why A is true since the path independence is due to the conservative nature of central forces, not the lack of potential energy in all forces.