JEE Physics 2025 Question with Solution

Given: Assertion A states that in a central force field, the work done is independent of the path chosen. Reason R states that every force encountered in mechanics does not have an associated potential energy.

Find: Which option correctly describes the truth of A and R, and whether R explains A.

A central force is a conservative force. For a conservative force, the work done depends only on the initial and final positions and not on the path followed.

Therefore, Assertion A is true.

Reason R is also true because not every force in mechanics has an associated potential energy. Non-conservative forces such as friction and air resistance do not have a well-defined potential energy since their work depends on the path.

However, R does not explain A. The path independence in Assertion A is due to the conservative nature of central forces, whereas Reason R is only a general statement that some forces do not have associated potential energy.

Therefore, both A and R are true, but R is not the correct explanation of A. The correct option is C.

Given:

• 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.

Find: The most appropriate relation between Assertion A and Reason R.

Step 1: Understand Assertion A. A central force acts along the line joining the particle and a fixed point, and its magnitude depends only on the distance from that point. Examples include gravitational and electrostatic forces.

Step 2: Use the relevant principle. Central forces are conservative. For conservative forces, work done is path independent and depends only on the initial and final positions.

So, Assertion A is true.

Step 3: Examine Reason R. Not all forces in mechanics are conservative. Forces like friction and viscous drag are non-conservative, so an associated potential energy function cannot be defined for them.

So, Reason R is also true.

Step 4: Check whether R explains A. Assertion A is true because a central force is conservative. Reason R says only that some mechanical forces do not have associated potential energy. This does not explain why work in a central force field is path independent.

Conclusion: Both A and R are true, but R is not the correct explanation of A. Hence, the correct option is C.