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MCQEasyJEE 2025Non-Conservative Forces

JEE Physics 2025 Question with Solution

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

  • A

    Coulomb's force

  • B

    Gravitational force

  • C

    Frictional force

  • D

    Restoring force

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given: The forces listed are Coulomb's force, gravitational force, frictional force, and restoring force.

Find: Which force cannot be expressed in terms of potential energy.

A force can be expressed in terms of potential energy only if it is conservative. For a conservative force,

F⃗=−∇U\vec{F} = -\nabla U

or in one dimension,

F=−dUdxF = -\frac{dU}{dx}

Also, the work done by a conservative force is path-independent.

Now analyze each force:

  1. Coulomb's force is conservative, and its potential energy is
U=kq1q2rU = \frac{k q_1 q_2}{r}
  1. Gravitational force is conservative, and its potential energy is
U=−Gm1m2rU = -\frac{G m_1 m_2}{r}
  1. Restoring force such as spring force is conservative, and its potential energy is
U=12kx2U = \frac{1}{2} k x^2
  1. Frictional force is non-conservative. Its work depends on the path taken, and it dissipates mechanical energy as heat. Therefore, it cannot be represented by a potential energy function.

Therefore, the force that cannot be expressed in terms of potential energy is frictional force.

The correct option is C.

Concept-Based Analysis

Given: We must identify which listed force does not admit a potential energy description.

Find: The non-conservative force among the options.

The key idea is that only conservative forces have a well-defined potential energy. For such forces, the work done between two points depends only on the initial and final positions, not on the path.

  • Coulomb's force: conservative.
  • Gravitational force: conservative.
  • Restoring force: conservative.
  • Frictional force: non-conservative.

Friction opposes motion and converts mechanical energy into heat. Since its work depends on the path length, it cannot be written in terms of a single-valued potential energy function.

Hence, frictional force is the required answer, so the correct option is C.

Common mistakes

  • Assuming every force has an associated potential energy. This is wrong because only conservative forces can be derived from a potential energy function. First check whether the work done is path-independent.

  • Confusing restoring force with a non-conservative force. This is incorrect because the spring restoring force is conservative and has elastic potential energy. Use the spring energy relation instead of classifying it by everyday intuition.

  • Ignoring the path dependence of friction. This is wrong because friction does different work along different paths and dissipates energy as heat. Test the force using the criterion of work over a closed path.

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