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 accurate: in a central force field (e.g., gravitational or electrostatic), forces are conservative, making work done path-independent. Statement R is partially true; not all forces (e.g., friction) possess potential energy. However, R does not correctly justify A's truthfulness, as the path independence of central forces stems from their conservative nature, not from the absence of potential energy in all forces.