Identify Force Not Expressed by Potential Energy

 

❓ Question

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

• Gravitational force

• Restoring force

• Frictional force

• Coulomb's force

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🖼️ Question Image

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✍️ Short Explanation

This problem is based on:

👉 Conservative forces
👉 Potential energy
👉 Work-energy theorem.

Main idea:

Only conservative forces can be represented using potential energy.

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🔷 Step 1 — Potential Energy Concept 💯

A force can be expressed through potential energy if:

$$\boxed{ \vec F=-\frac{dU}{dx} }$$

Such forces are called:

$$\boxed{ \text{Conservative forces} }$$

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🔷 Step 2 — Check Each Force

(1) Gravitational force

Has potential energy:

$$U=-\frac{GMm}{r}$$

✔ Conservative force

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(2) Restoring force

For spring:

$$F=-kx$$

Potential energy:

$$U=\frac12kx^2$$

✔ Conservative force

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(3) Frictional force

Friction depends on path and dissipates energy as heat.

❌ No unique potential energy function exists.

Thus friction is:

$$\boxed{ \text{Non-conservative} }$$

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(4) Coulomb’s force

Potential energy:

$$U=\frac{kq_1q_2}{r}$$

✔ Conservative force

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🔷 Step 3 — Final Logic

Only frictional force cannot be represented using potential energy.

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🔷 Step 4 — JEE Trap Alert 🚨

❌ Every force ko conservative maan lena

❌ Restoring force ko non-conservative samajhna

❌ Path dependence concept bhool jaana

Remember:

$$\boxed{ \text{Non-conservative force} \Rightarrow \text{No potential energy function} }$$

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✅ Final Answer

$$\boxed{ \text{Frictional force} }$$

(Option 3)

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