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Work Power and Energy question

2025 · 7 Apr · Shift 2 · Q55
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Work Power and Energy question

2025 · 7 Apr · Shift 2 · Q55

JEE MainPhysicsWork Power and EnergyMCQ+4 / −1
Which one of the following forces cannot be expressed in terms of potential energy?
  1. A
    Frictional force
  2. B
    Coulomb’s force
  3. C
    Restoring force
  4. D
    Gravitational force
View written solutionFree

Correct answer: A

  1. Concept used: Conservative vs non-conservative force

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

For a conservative force,

F⃗=−∇U\vec{F} = -\nabla UF=−∇U

where UUU is the potential energy.

So we check which given force is not conservative.

  1. Check each option

(A) Frictional force

Friction depends on the path and dissipates mechanical energy into heat. Work done by friction over a closed path is not zero.

Hence, friction is a non-conservative force, so it cannot generally be expressed in terms of a potential energy function.

(B) Coulomb’s force

Electrostatic Coulomb force is conservative. Its potential energy is

U=14πε0q1q2rU = \frac{1}{4\pi \varepsilon_0}\frac{q_1 q_2}{r}U=4πε0​1​rq1​q2​​

So it can be expressed in terms of potential energy.

(C) Restoring force

For example, spring restoring force is

F=−kxF = -kxF=−kx

Its potential energy is

U=12kx2U = \frac{1}{2}kx^2U=21​kx2

So restoring force can be expressed in terms of potential energy.

(D) Gravitational force

Gravitational force is conservative. Near Earth,

U=mghU = mghU=mgh

and in general,

U=−GMmrU = -\frac{GMm}{r}U=−rGMm​

So it can be expressed in terms of potential energy.

  1. Conclusion

The only force among the options that cannot be expressed in terms of potential energy is:

A: Frictional force\boxed{\text{A: Frictional force}}A: Frictional force​
  1. Comparison with stored correct answer

Stored correct answer: AAA

Our derived answer is also AAA, so they match.

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