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

Assertion A: In a central force field, the work done is independent of the path chosen. This statement is true.
Central forces are conservative forces, and the work done by a conservative force depends only on the initial and final positions, not on the path taken.

Reason R: Every force encountered in mechanics does not have an associated potential energy. This statement is also true. Non-conservative forces like friction and air resistance do not have associated potential energies because the work done by these forces depends on the path taken.

Analysis of the Relationship Between A and R:

• The independence of work done on the path depends on the fact that the force is conservative.
• All conservative forces possess an associated potential energy function.
• Since Reason R states that not every force has an associated potential energy, while Assertion A refers specifically to conservative (central) forces which do have potential energy,
• Reason R is not a correct explanation of Assertion A — it makes a general statement about forces, not specifically about central or conservative forces.

Therefore, both A and R are true, but R is NOT the correct explanation of A.

Final Answer:
The final answer is $ (2)\ \text{Both A and R are true but R is NOT the correct explanation of A} $.