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Physics Question 30 – JEE-MAIN 2025

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Which one of the following forces cannot be expressed in terms of potential energy ?

Potential energy is defined only for conservative forces.

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Ninja Strategy•Identify Non-Conservative Force

Recall that potential energy is only defined for conservative forces; frictional force is the only non-conservative option.

Step 1: Understand Potential Energy and Forces✦ Active

Potential energy is a concept associated with conservative forces. A force F is conservative if the work done by it is independent of the path taken, and it can be expressed as the negative gradient of a scalar potential energy function U, i.e., F=−∇U.

Step 2: Classify the Given Forces○ Expand

1. Coulomb's force (electrostatic force) is a conservative force. The work done by it depends only on the initial and final positions of the charges. It is associated with electric potential energy.

2. Gravitational force is a conservative force. The work done by gravity depends only on the change in vertical height. It is associated with gravitational potential energy.

3. Restoring force (e.g., spring force) is a conservative force. The work done by a spring depends only on the initial and final extensions/compressions. It is associated with elastic potential energy.

4. Frictional force is a non-conservative force. The work done by friction depends on the path length and always opposes motion, converting mechanical energy into heat. It cannot be expressed in terms of a potential energy function.

Step 3: Identify the Force Not Expressible by Potential Energy○ Expand

Based on the classification, frictional force is the only non-conservative force among the options. Therefore, it cannot be expressed in terms of potential energy.

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