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: The work done by a central force is path-independent. This assertion is correct. Central forces are a subset of conservative forces, and the work performed by conservative forces is solely contingent upon the initial and final positions, irrespective of the trajectory traversed.

Reason R: Not all mechanical forces are associated with a potential energy function. This reason is also correct. Forces classified as non-conservative, such as friction and air resistance, lack associated potential energies because the work they perform is path-dependent.

Analysis of the Relationship Between A and R:

• The path-independent nature of work is characteristic of conservative forces.
• All conservative forces are associated with a potential energy function.
• Reason R makes a general claim about forces, stating that not all forces have potential energy. Assertion A, however, specifically addresses central forces, which are conservative and thus do possess associated potential energies.
• Consequently, Reason R does not correctly explain Assertion A; it is a broader statement that does not specifically relate to the properties of central or conservative forces.

Therefore, both Assertion A and Reason R are true statements, but Reason R does not provide a correct explanation for Assertion A.

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