Potential Energy of a Spring Notes for NEET 2026 | Hooke's Law Explained

-  Dr.Sanjaykumar pawar 

Potential Energy of a Spring Class 11 Physics Notes for NEET

Potential Energy of a Spring explained with Hooke's Law, formulas, graphs, and NEET exam shortcuts.

Internal Links

• Work, Energy and Power Complete Notes
• Work Done by Variable Force
• Conservative and Non-Conservative Forces
• Kinetic Energy Theorem
• Power and Efficiency
• Mechanical Energy Conservation
• Circular Motion Notes
• Simple Harmonic Motion (SHM)
• Oscillations Complete Notes
• Elasticity and Stress-Strain
• Rotational Motion Notes
• Gravitation Notes
• Laws of Motion 
• Motion in One Dimension
• Motion in Two Dimensions
• Friction Notes
• NCERT Class 11 Physics Notes
• NEET Physics Formula Handbook
• NEET Physics MCQs with Solutions
• Previous Year NEET Physics Questions

NEET Physics Notes

Potential Energy of a Spring (Hooke's Law)

1. Introduction

A spring is an elastic object that returns to its original shape after stretching or compressing.

Examples

• Pen Spring
• Vehicle Shock Absorber
• Spring Balance
• Toy Spring

NEET Point: Spring force is a restoring force.

2. Hooke's Law

The restoring force of a spring is directly proportional to the displacement from its equilibrium position.

F = -kx

Symbol	Meaning	SI Unit
F	Restoring Force	Newton (N)
k	Spring Constant	N/m
x	Displacement	m

Negative sign shows that the spring force always acts opposite to displacement.

3. Spring Constant (k)

The spring constant measures the stiffness of a spring.

Large k	Small k
Hard Spring	Soft Spring

SI Unit

N/m

Dimension

M T^-2

4. Force-Displacement Graph

The graph between force and displacement is a straight line passing through the origin.

Slope = -k

Area under the Force-Displacement graph gives the work done.

5. Work Done by External Force

To stretch the spring slowly from 0 to x, the external force acts in the same direction as displacement.

F = kx

Work done

W = ∫F dx

W = ½kx²

This energy gets stored as Potential Energy inside the spring.

6. Work Done by Spring

Since spring force acts opposite to displacement, its work is negative.

W = -½kx²

External Force → Positive Work

Spring Force → Negative Work

16. NEET Practice MCQs

1. According to Hooke's law, spring force is
   • A. Constant
   • B. Proportional to displacement ✔
   • C. Inversely proportional to displacement
   • D. Zero
   Answer: B
2. The SI unit of spring constant is
   • A. N
   • B. J
   • C. N/m ✔
   • D. Nm
   Answer: C
3. Potential energy stored in a spring is
   U = ½kx²
4. At equilibrium position,
   • A. KE Maximum ✔
   • B. PE Maximum
   • C. Both Zero
   • D. Speed Zero
5. Total mechanical energy is
   • A. Variable
   • B. Constant ✔
   • C. Infinite
   • D. Zero

17. Assertion – Reason Questions

Q1.

Assertion: Spring force is a restoring force.

Reason: Spring force acts opposite to displacement.

Both Assertion and Reason are true, and Reason correctly explains Assertion.

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Q2.

Assertion: Potential energy is zero at equilibrium.

Reason: Displacement is zero.

Both are true.

18. Previous Year NEET Questions

Question 1

A spring is stretched by x. Potential energy becomes

• A. kx
• B. kx²
• C. ½kx² ✔
• D. 2kx²

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Question 2

The slope of Force-Displacement graph equals

• A. k
• B. -k ✔
• C. 1/k
• D. Zero

19. One Minute Revision

Concept	Formula
Hooke's Law	F = -kx
Potential Energy	½kx²
Work by Spring	-½kx²
Mechanical Energy	K + U
Maximum Speed	xₘ√(k/m)
Maximum Compression	v√(m/k)

20. Quick NEET Tips

• Remember the negative sign in Hooke's law.
• Potential energy depends on x².
• Spring force always opposes displacement.
• KE is maximum at mean position.
• PE is maximum at extreme positions.
• Total mechanical energy remains constant.
• Hooke's law is valid only within the elastic limit.
• Area under F-x graph represents work done.

NEET Physics Notes

Potential Energy of a Spring

Prepared for Beginners

Happy Learning 📘

16. NEET Practice MCQs

CBSE Class 11 Physics

Chapter: Work, Energy and Power

Topic: Potential Energy of a Spring (Hooke's Law)

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1. Multiple Choice Questions (MCQs)

1. The restoring force of a spring is
   A) kx
   B) -kx
   C) x/k
   D) k/x

   Answer: B

2. SI unit of spring constant is
   A) N
   B) J
   C) N/m
   D) Nm

   Answer: C

3. Potential energy stored in a spring is
   A) kx
   B) k/x
   C) ½kx²
   D) k²x

   Answer: C

4. At equilibrium position, spring potential energy is
   A) Maximum
   B) Minimum
   C) Infinite
   D) Negative

   Answer: B

5. Hooke's law is valid only within
   A) Elastic limit
   B) Plastic limit
   C) Breaking point
   D) Melting point

   Answer: A

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2. Very Short Answer Questions (1 Mark)

1. State Hooke's Law.

   Within elastic limit, restoring force is directly proportional to displacement.

2. Write the formula of spring force.

   F = -kx

3. What is the SI unit of spring constant?

   Newton per metre (N/m)

4. Write the formula of spring potential energy.

   U = ½kx²

5. At which position is kinetic energy maximum?

   At the equilibrium position.

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3. Short Answer Questions (2–3 Marks)

1. Why is the spring force negative?

   The negative sign shows that the restoring force acts opposite to the displacement and always tries to bring the spring back to equilibrium.

2. Derive the expression for work done by stretching a spring.

   W = ∫Fdx = ∫kx dx = ½kx²

3. Define spring constant.

   Spring constant is the force required to produce unit displacement in a spring.

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4. Long Answer Questions (5 Marks)

1. Derive the expression for the potential energy stored in a spring.

   Given, F = kx Work done, W = ∫Fdx = ∫kx dx = ½kx² Hence, Potential Energy, U = ½kx²

2. State and explain conservation of mechanical energy in a spring block system.

   Total Energy E = K + U = ½mv² + ½kx² The total mechanical energy remains constant.

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5. Assertion and Reason

Q1.

Assertion (A): Spring force is a restoring force.

Reason (R): Spring force always acts opposite to displacement.

Answer: Both Assertion and Reason are true and Reason correctly explains Assertion.

Q2.

Assertion: Potential energy of spring is maximum at equilibrium.

Reason: Velocity is maximum at equilibrium.

Answer: Assertion is False, Reason is True.

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6. Fill in the Blanks

1. Spring force is ______ proportional to displacement.

   Directly

2. Hooke's law is F = ______

   -kx

3. Potential energy stored in spring is ______

   ½kx²

4. The SI unit of spring constant is ______

   N/m

5. Mechanical energy is the sum of kinetic and ______ energy.

   Potential

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7. True / False

1. Spring force always acts opposite to displacement.

   True

2. Potential energy is maximum at equilibrium.

   False

3. Hooke's law is valid within elastic limit.

   True

4. Spring constant is measured in joule.

   False

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8. Match the Columns

Column A	Column B
Hooke's Law	F = -kx
Spring Potential Energy	½kx²
SI Unit of k	N/m
Equilibrium Position	PE = 0

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9. Case Study Questions

A block is attached to a spring fixed at one end. The block is pulled by 20 cm and released. The spring constant is 200 N/m.

Q1. Write Hooke's law.

F = -kx

Q2. Calculate potential energy stored.

x = 0.20 m U = ½kx² = ½ × 200 × (0.20)² = 4 J

Q3. At which position is kinetic energy maximum?

At equilibrium position.

Q4. At which position is potential energy maximum?

At maximum extension or compression.

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10. Important Formula Sheet

• Hooke's Law: F = -kx
• Work Done: W = ½kx²
• Potential Energy: U = ½kx²
• Total Mechanical Energy: E = K + U
• Maximum Speed: v = xm√(k/m)
• Maximum Compression: x = v√(m/k)

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End of Question Bank