NCERT Physics Class 11 Example 5.8 & 5.9 Solutions | Spring Compression Explained

 - Dr.Sanjaykumar Pawar 

A moving car compresses a spring, demonstrating conservation of mechanical energy and work-energy theorem.

Internal Links

• NCERT Class 11 Physics Chapter 5 Notes
• Work, Energy and Power Formulas
• Conservation of Mechanical Energy
• Work-Energy Theorem Explained
• Hooke's Law and Spring Force
• Potential Energy and Kinetic Energy
• NCERT Physics Example 5.1–5.7 Solutions
• NCERT Physics Chapter 5 Exercise Solutions
• JEE Physics Work Energy Questions
• NEET Physics Chapter-wise MCQs
• Energy Conservation Numerical Problems
• Class 11 Physics Formula Sheet

NCERT Physics Class 11

Chapter 5 - Work, Energy and Power

Example 5.8 & Example 5.9

Question 1

A car of mass 1000 kg is moving with a speed of 18 km h^-1 on a smooth horizontal road and collides with a spring of spring constant 5.25 × 10³ N m^-1. Find the maximum compression of the spring.

Answer

Given

• Mass (m) = 1000 kg
• Speed (v) = 18 km h^-1 = 5 m s^-1
• Spring constant (k) = 5.25 × 10³ N m^-1

Formula

At maximum compression,

Kinetic Energy = Spring Potential Energy

½mv² = ½kx²

Step 1 : Calculate Kinetic Energy

K = ½ × 1000 × 5²

K = 12500 J

Step 2 : Calculate Compression

12500 = ½ × 5.25 × 10³ × x²

12500 = 2625x²

x² = 12500 / 2625

x² = 4.76

x = √4.76

x ≈ 2.18 m

Maximum Compression = 2.0 m (Approx.)

---

Question 2

Using Example 5.8, if the coefficient of friction is 0.5, calculate the maximum compression of the spring.

Answer

Given

• Mass = 1000 kg
• Speed = 5 m s^-1
• Spring constant = 5.25 × 10³ N m^-1
• Coefficient of friction = 0.5
• g = 10 m s^-2

Formula

Work-Energy Theorem

ΔK = W

½mv² = ½kx² + μmgx

Step 1

12500 = 2625x² + 5000x

Step 2

2625x² + 5000x − 12500 = 0

Step 3

Using quadratic formula,

x = 1.35 m

Maximum Compression = 1.35 m

---

Practice Questions

Practice Question 1

A spring of spring constant 400 N m^-1 is compressed by 0.5 m. Calculate the elastic potential energy stored.

Formula

U = ½kx²

U = ½ × 400 × (0.5)²

U = 50 J

Answer = 50 J

Practice Question 2

A body of mass 2 kg moves with speed 10 m s^-1. Find its kinetic energy.

Formula

K = ½mv²

K = ½ × 2 × 10²

K = 100 J

Answer = 100 J

Practice Question 3

A spring stores 100 J of energy. Its spring constant is 500 N m^-1. Find the compression.

100 = ½ × 500 × x²

100 = 250x²

x² = 0.4

x = 0.63 m

Answer = 0.63 m

Practice Question 4

A 500 kg car moving at 10 m s^-1 hits a spring of spring constant 10000 N m^-1. Find the maximum compression.

K = ½mv²

K = ½ × 500 × 10²

K = 25000 J

25000 = ½ × 10000 × x²

25000 = 5000x²

x² = 5

x = 2.24 m

Answer = 2.24 m

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Important Formulae

Formula	Expression
Kinetic Energy	K = ½mv²
Spring Potential Energy	U = ½kx²
Work-Energy Theorem	ΔK = W
Mechanical Energy	KE + PE = Constant (Without Friction)

---

Important Viva Questions

1. Why does the car stop at maximum compression?
   Because all kinetic energy is converted into spring potential energy.


2. Why is conservation of mechanical energy not applicable when friction is present?
   Because friction is a non-conservative force and converts mechanical energy into heat.


3. What is the formula of spring potential energy?
   U = ½kx²


4. What is the formula of kinetic energy?
   K = ½mv²

NEET Physics Notes

Chapter: Work, Energy and Power

Topics Covered

• Spring Force (Hooke's Law)
• Spring Potential Energy
• Kinetic Energy
• Conservation of Mechanical Energy
• Work-Energy Theorem
• Friction
• NCERT Example 5.8
• NCERT Example 5.9
• Important Formulae
• NEET MCQs

1. Spring Force (Hooke's Law)

When a spring is stretched or compressed, it tries to return to its original length. This restoring force is called Spring Force.

Formula

F = -kx

Symbol	Meaning
F	Spring Force (N)
k	Spring Constant (N/m)
x	Compression or Extension (m)

Remember

• Negative sign shows restoring force.
• Force acts opposite to displacement.
• Larger k means stronger spring.
• Smaller k means softer spring.

2. Spring Potential Energy

Energy stored inside a compressed or stretched spring.

Formula

U = ½ kx²

Symbol	Meaning
U	Potential Energy
k	Spring Constant
x	Compression

3. Kinetic Energy

Energy possessed by a moving object.

Formula

K = ½ mv²

Symbol	Meaning
m	Mass
v	Velocity

4. Conservation of Mechanical Energy

When there is no friction, the total mechanical energy remains constant.

½mv² = ½kx²

Used to calculate maximum compression of a spring.

Example 5.8

To simulate car accidents, auto manufacturers study the collisions of moving cars with mounted springs and other constraints. Consider a typical simulation with a car of mass 1000 kg moving at a speed of 18.0 km/h on a smooth road and colliding with a horizontal mounted spring of spring constant 5.25 × 10³ N m⁻¹. What is the maximum compression of the spring?

Example 5.9

Consider Example 5.8 taking the coefficient of friction, μ = 0.5, and calculate the maximum compression of the spring.

NCERT Example 5.8

Question

Mass = 1000 kg
Speed = 18 km/h
Spring Constant = 5.25 × 10³ N/m
Find the maximum compression.

Solution

Step 1 18 km/h = 5 m/s

Kinetic Energy

K = ½ ×1000×5²

K = 12500 J

Using Conservation of Energy

½kx² = 12500

x = 2.0 m

Answer: Maximum Compression = 2.0 m

5. Work-Energy Theorem

The work done by all forces acting on a body equals the change in kinetic energy.

Formula

W = ΔK

6. Friction

Friction always opposes motion.

Formula

F = μN

On horizontal surface,

N = mg

Therefore,

F = μmg

NCERT Example 5.9

Question

Mass = 1000 kg
Speed = 5 m/s
k = 5.25 ×10³ N/m
μ = 0.5

Solution

Apply Work-Energy Theorem

−½mv² = −½kx² − μmgx

Rearranging,

kx² + 2μmgx − mv² = 0

x = 1.35 m

Answer: Maximum Compression = 1.35 m

Important Formula Sheet

Formula	Equation
Kinetic Energy	½mv²
Spring Force	F = -kx
Spring Potential Energy	½kx²
Friction	μmg
Work-Energy Theorem	W = ΔK
Conservation of Energy	½mv² = ½kx²

NEET Important Points

• Hooke's law is valid only within elastic limit.
• Spring force is a restoring force.
• Potential energy is always positive.
• Friction is a non-conservative force.
• Mechanical energy is conserved only without friction.
• Work done by friction is negative.
• Spring energy depends on x².
• Kinetic energy depends on velocity².

NEET Practice MCQs

Q1. The force exerted by a spring is

• A. Constant
• B. Proportional to displacement
• C. Inversely proportional
• D. Zero

Answer: B

Q2. Potential energy stored in a spring is

• A. kx
• B. kx²
• C. ½kx²
• D. ½kx

Answer: C

Q3. Which force is non-conservative?

• A. Gravity
• B. Spring
• C. Electrostatic
• D. Friction

Answer: D

Q4. Mechanical energy remains constant when

• A. Friction acts
• B. Air resistance acts
• C. Only conservative forces act
• D. External work is done

Answer: C

Quick Revision

• Hooke's Law → F = -kx
• Spring Energy → ½kx²
• Kinetic Energy → ½mv²
• Work-Energy Theorem → W = ΔK
• Without friction → Energy conserved.
• With friction → Use Work-Energy Theorem.
• Maximum compression occurs when kinetic energy becomes zero.
• Friction reduces spring compression.

---

Prepared for NEET Aspirants

Easy Notes • NCERT Based • Beginner Friendly

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.

---

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

---

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)

---

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

---

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.

---

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.

---

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.

---

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.

---

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

---

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

---

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

---

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.

---

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)

---

End of Question Bank

The Concept of Potential Energy Notes for NEET 2026 | Class 11 Physics Chapter 5.7

 - Dr.Sanjaykumar Pawar 

Gravitational Potential Energy Notes for NEET with Formula & Examples

Gravitational Potential Energy (PE = mgh) and its conversion into kinetic energy explained with simple examples for NEET students.

Internal Links

Work, Energy and Power Complete Notes

Kinetic Energy Formula and Derivation

Work Done by a Constant Force

Conservative and Non-Conservative Forces

Law of Conservation of Mechanical Energy

Power in Physics Notes

Motion in a Straight Line Notes

Newton's Laws of Motion Notes

Gravitation Complete Notes

Acceleration Due to Gravity (g) Notes

Escape Velocity Notes

Circular Motion Notes

Mechanical Properties of Solids

Rotational Motion Notes

Oscillations and Simple Harmonic Motion

NEET Physics Formula Handbook

Class 11 Physics Chapter-wise Notes

Most Important NEET Physics MCQs

Previous Year NEET Physics Questions

NCERT Physics Chapter 5 Summary

NEET Physics Notes

Chapter 5.7 – The Concept of Potential Energy

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1. Meaning of Potential Energy

The word Potential means the ability or capacity to do work in the future.

Potential Energy (PE) is the energy stored in a body because of its position or shape (configuration).

Definition

Potential Energy is the energy possessed by a body due to its position or configuration.

---

2. Everyday Examples

Example 1 – Stretched Bow

• A stretched bow stores energy.
• When the string is released, stored energy changes into kinetic energy.
• The arrow moves with high speed.

Example 2 – Earthquake

• The Earth's crust has cracks called fault lines.
• These fault lines store a large amount of energy.
• When they suddenly move, the stored energy is released.
• This causes an earthquake.

Potential Energy is stored energy that can later change into kinetic energy.

---

3. Gravitational Potential Energy

Consider a ball of mass m near the Earth's surface.

Assumption

• Acceleration due to gravity (g) remains constant.
• Height (h) is much smaller than Earth's radius.

\[ h \ll R_E \]

Where

• h = height of object
• R_E = radius of Earth

---

4. Raising a Ball

Suppose a ball is lifted upward through height h.

• Gravity acts downward.
• An external force is required to lift the ball.
• Work is done against gravity.

\[ W = mgh \]

This work gets stored as gravitational potential energy.

---

5. Formula of Gravitational Potential Energy

\[ PE = V(h)=mgh \]

Where

• m = mass
• g = acceleration due to gravity
• h = height

---

6. Important Points

• Greater height → Greater Potential Energy.
• Greater mass → Greater Potential Energy.
• If h = 0, then Potential Energy = 0.

---

7. Relation Between Force and Potential Energy

\[ F=-\frac{dV}{dh} \]

Since

\[ V=mgh \]

Differentiate,

\[ \frac{dV}{dh}=mg \]

Therefore,

\[ F=-mg \]

The negative sign shows that gravity always acts downward.

---

8. Conversion of Potential Energy into Kinetic Energy

When the ball is released:

• Potential Energy decreases.
• Kinetic Energy increases.
• At the ground, Potential Energy becomes minimum.
• Kinetic Energy becomes maximum.

---

9. Speed of Falling Ball

Using the equation of motion,

\[ v^2=u^2+2gh \]

Since

\[ u=0 \]

Therefore,

\[ v^2=2gh \]

---

10. Kinetic Energy at Ground

\[ KE=\frac12 mv^2 \]

Substitute

\[ v^2=2gh \]

\[ KE=\frac12 m(2gh) \]

\[ KE=mgh \]

Hence,

\[ PE=KE \]

---

11. When Does Potential Energy Exist?

Potential Energy exists only for Conservative Forces.

Examples

• Gravitational Force
• Spring Force
• Electrostatic Force

---

12. Conservative Force

A Conservative Force is a force whose work depends only on the initial and final positions and not on the path followed.

Examples

• Gravity
• Spring Force
• Electrostatic Force

---

13. Mathematical Definition

\[ F(x)=-\frac{dV}{dx} \]

Potential Energy exists only if the force satisfies this equation.

---

14. Work Done by Conservative Force

\[ \int_{x_i}^{x_f}F(x)\,dx =-(V_f-V_i) \]

or

\[ W=V_i-V_f \]

Meaning:

Work done by a conservative force equals the decrease in Potential Energy.

---

15. Change in Potential Energy

\[ \Delta V=-W \]

Meaning

• If gravity does positive work, Potential Energy decreases.
• If work is done against gravity, Potential Energy increases.

---

16. Inclined Plane Example

A body slides from the top of a smooth inclined plane of height h.

Its speed at the bottom is

\[ v=\sqrt{2gh} \]

This speed depends only on height and not on the angle of inclination.

---

17. Kinetic Energy at Bottom

\[ KE=\frac12 mv^2 \]

Substitute

\[ v^2=2gh \]

\[ KE=mgh \]

Hence,

Loss of Potential Energy = Gain of Kinetic Energy

---

18. Non-Conservative Force

A Non-Conservative Force is a force whose work depends on the path followed.

Examples

• Friction
• Air Resistance
• Viscous Force

---

19. Dimensions of Potential Energy

\[ [ML^2T^{-2}] \]

---

20. SI Unit

Joule (J)

---

21. Energy Conversion

Potential Energy can convert into

• Kinetic Energy
• Heat Energy
• Sound Energy

---

22. Important NEET Formula Sheet

Formula	Expression
Gravitational Potential Energy	\(PE=mgh\)
Force and Potential Energy	\(F=-\frac{dV}{dh}\)
General Relation	\(F=-\frac{dV}{dx}\)
Work Done	\(W=V_i-V_f\)
Change in Potential Energy	\(\Delta V=-W\)
Speed of Falling Body	\(v=\sqrt{2gh}\)
Kinetic Energy	\(KE=\frac12 mv^2\)
At Ground	\(KE=mgh\)

---

23. NEET One-Line Revision

• Potential Energy is stored energy.
• It depends on position or configuration.
• Gravitational Potential Energy = mgh.
• Gravity is a conservative force.
• \(F=-\frac{dV}{dx}\)
• \(\Delta V=-W\)
• Potential Energy decreases when gravity does work.
• Potential Energy converts into Kinetic Energy during free fall.
• On a frictionless inclined plane, speed depends only on height.
• SI Unit = Joule (J).
• Dimensions = \([ML^2T^{-2}]\)
• Mechanical Energy remains conserved when only conservative forces act.

End of Chapter 5.7 – The Concept of Potential Energy

CBSE Class 11 Physics

Chapter 5.7 – The Concept of Potential Energy

Part 1 : MCQs & Very Short Answer Questions

Section A : Multiple Choice Questions (MCQs)

1. Potential energy is the energy possessed by a body due to its:

1. Speed
2. Mass
3. Position or configuration
4. Temperature

Answer: (c) Position or configuration

2. The SI unit of potential energy is:

1. Newton
2. Joule
3. Watt
4. Pascal

Answer: (b) Joule

3. Gravitational potential energy of a body is:

1. mg
2. gh
3. mgh
4. mv²

Answer: (c) mgh

4. The dimensional formula of potential energy is:

1. [MLT⁻²]
2. [ML²T⁻²]
3. [ML²T⁻¹]
4. [MLT]

Answer: (b) [ML²T⁻²]

5. Potential energy depends upon:

1. Speed
2. Position or configuration
3. Momentum
4. Temperature

Answer: (b) Position or configuration

6. Which of the following is a conservative force?

1. Friction
2. Air resistance
3. Gravity
4. Viscous force

Answer: (c) Gravity

7. The relation between force and potential energy is:

1. F = dV/dx
2. F = –dV/dx
3. F = V/x
4. F = Vx

Answer: (b) F = –dV/dx

8. If the height of an object is doubled, its gravitational potential energy becomes:

1. Half
2. Double
3. Four times
4. Zero

Answer: (b) Double

9. At ground level, the potential energy is generally taken as:

1. Infinity
2. mgh
3. Zero
4. mg

Answer: (c) Zero

10. During free fall:

1. Potential energy increases
2. Kinetic energy decreases
3. Potential energy converts into kinetic energy
4. Both energies remain constant

Answer: (c) Potential energy converts into kinetic energy

Section B : Very Short Answer Questions (1 Mark)

1. Define potential energy.

Potential energy is the energy possessed by a body due to its position or configuration.

2. Write the SI unit of potential energy.

Joule (J)

3. Write the dimensional formula of potential energy.

[ML²T⁻²]

4. Write the formula of gravitational potential energy.

PE = mgh

5. What is a conservative force?

A conservative force is a force whose work depends only on the initial and final positions and not on the path followed.

6. Name one conservative force.

Gravitational force.

7. Name one non-conservative force.

Frictional force.

8. Write the relation between force and potential energy.

F = –dV/dx

9. What is gravitational potential energy?

It is the energy possessed by a body due to its position above the Earth's surface.

10. What happens to potential energy during free fall?

Potential energy decreases and converts into kinetic energy.

11. Write the expression for kinetic energy.

KE = ½mv²

12. State the law of conservation of mechanical energy.

When only conservative forces act on a body, the total mechanical energy (Potential Energy + Kinetic Energy) remains constant.

13. Give one example of stored energy.

A stretched spring or a stretched bow.

14. Does potential energy depend upon velocity?

No. It depends only on position or configuration.

15. Write the mathematical relation for change in potential energy.

ΔV = –W

End of Part 1
Next: Part 2 – Short Answer & Long Answer Questions

CBSE Class 11 Physics

Chapter 5.7 – The Concept of Potential Energy

Part 2 : Short Answer & Long Answer Questions

Section C : Short Answer Questions (2–3 Marks)

1. Define potential energy. Explain with one example.

Potential energy is the energy possessed by a body due to its position or configuration. Example: A stretched bow stores potential energy. When the string is released, the stored potential energy changes into kinetic energy and the arrow moves with high speed.

2. Derive the expression for gravitational potential energy.

Consider a body of mass m lifted vertically through a height h. Weight of body = mg Work done against gravity

W = Force × Distance

W = mg × h

W = mgh

This work is stored as gravitational potential energy. Therefore,

PE = mgh

3. Why is gravitational force called a conservative force?

Gravitational force is called a conservative force because:

• Its work depends only on the initial and final positions.
• It does not depend on the path followed.
• Mechanical energy remains conserved when only gravity acts.

4. What happens to potential energy during free fall?

During free fall:

• Potential energy decreases.
• Kinetic energy increases.
• Total mechanical energy remains constant.

Thus, potential energy is converted into kinetic energy.

5. Differentiate between conservative and non-conservative forces.

Conservative Force	Non-Conservative Force
Work depends only on initial and final positions.	Work depends on the path followed.
Mechanical energy is conserved.	Mechanical energy is not conserved.
Example: Gravity	Example: Friction

6. Explain the relation between force and potential energy.

For a conservative force,

\[ F=-\frac{dV}{dx} \]

The negative sign shows that the force acts in the direction of decreasing potential energy.

Section D : Long Answer Questions (5 Marks)

1. Explain gravitational potential energy and derive its formula.

Potential energy is the stored energy possessed by a body because of its position. Suppose a body of mass m is lifted vertically upward through height h. Weight of the body

Force = mg

Work done

W = Force × Distance

W = mg × h

W = mgh

Since this work is stored as energy,

PE = mgh

Where

• m = Mass of the body
• g = Acceleration due to gravity
• h = Height above the ground

Therefore,

Gravitational Potential Energy = mgh

2. Explain how potential energy converts into kinetic energy during free fall.

Consider a body kept at a height h. Initially,

Potential Energy = mgh

When the body is released,

• Potential energy decreases.
• Kinetic energy increases.
• Total mechanical energy remains constant.

Using the equation of motion,

\[ v^2=2gh \]

Kinetic energy,

\[ KE=\frac12 mv^2 \]

Substituting,

\[ KE=\frac12 m(2gh) \]

\[ KE=mgh \]

Hence,

Potential Energy = Kinetic Energy

This proves the conservation of mechanical energy.

3. Explain the law of conservation of mechanical energy.

The law states: "When only conservative forces act on a body, the total mechanical energy remains constant." Mechanical Energy

Mechanical Energy = Potential Energy + Kinetic Energy

During free fall,

• Potential energy decreases.
• Kinetic energy increases.
• The total remains constant.

Therefore,

PE + KE = Constant

This is known as the law of conservation of mechanical energy.

4. A body of mass 5 kg is lifted to a height of 10 m. Calculate its gravitational potential energy. (Take g = 9.8 m/s²)

Given:

• Mass (m) = 5 kg
• Height (h) = 10 m
• g = 9.8 m/s²

Formula

PE = mgh

Calculation

PE = 5 × 9.8 × 10

PE = 490 J

Answer: The gravitational potential energy is 490 J.

5. State any five characteristics of potential energy.

1. Potential energy is stored energy.
2. It depends on position or configuration.
3. Its SI unit is Joule (J).
4. Its dimensional formula is [ML²T⁻²].
5. It can be converted into kinetic energy.

End of Part 2
Next: Part 3 – Assertion & Reason, Fill in the Blanks, Statement-Based Questions

CBSE Class 11 Physics

Chapter 5.7 – The Concept of Potential Energy

Part 3 : Assertion & Reason, Fill in the Blanks, Statement-Based Questions

Section E : Assertion and Reason Questions

Question 1

Assertion (A): Gravity is a conservative force.

Reason (R): Work done by gravity depends only on the initial and final positions.

Answer:
✔ Assertion is True.
✔ Reason is True.
✔ Reason is the correct explanation of the Assertion.

Question 2

Assertion (A): Potential energy decreases during free fall.

Reason (R): Kinetic energy increases during free fall.

Answer:
✔ Assertion is True.
✔ Reason is True.
✔ Reason correctly explains the Assertion.

Question 3

Assertion (A): Friction is a conservative force.

Reason (R): Work done by friction depends upon the path followed.

Answer:
✘ Assertion is False.
✔ Reason is True.

Question 4

Assertion (A): SI unit of potential energy is Joule.

Reason (R): Potential energy is a form of energy and work.

Answer:
✔ Assertion is True.
✔ Reason is True.
✔ Reason correctly explains the Assertion.

Question 5

Assertion (A): Potential energy depends upon velocity.

Reason (R): Potential energy depends upon position.

Answer:
✘ Assertion is False.
✔ Reason is True.

Section F : Fill in the Blanks

1. Potential energy depends upon the __________ of the body.

Answer: Position

2. The SI unit of potential energy is __________.

Answer: Joule (J)

3. Gravitational potential energy is equal to __________.

Answer: mgh

4. Gravity is a __________ force.

Answer: Conservative

5. Friction is a __________ force.

Answer: Non-conservative

6. During free fall, potential energy converts into __________ energy.

Answer: Kinetic

7. The dimensions of potential energy are __________.

Answer: [ML²T⁻²]

8. The relation between force and potential energy is __________.

Answer: F = −dV/dx

9. Potential energy is also called __________ energy.

Answer: Stored

10. Mechanical energy remains constant when only __________ forces act.

Answer: Conservative

Section G : Statement-Based Questions (True / False)

State whether the following statements are True or False.

1. Potential energy depends upon position.
Answer: True
2. Friction is a conservative force.
Answer: False
3. SI unit of potential energy is Joule.
Answer: True
4. Potential energy can be converted into kinetic energy.
Answer: True
5. Gravity is a conservative force.
Answer: True
6. Potential energy depends upon velocity.
Answer: False
7. Mechanical energy is conserved when only conservative forces act.
Answer: True
8. The dimensional formula of potential energy is [ML²T⁻²].
Answer: True
9. Potential energy is measured in Newton.
Answer: False
10. A stretched spring possesses potential energy.
Answer: True

Section H : Formula-Based Questions

1. Write the formula of gravitational potential energy.

PE = mgh

2. Write the relation between force and potential energy.

F = −dV/dx

3. Write the formula for change in potential energy.

ΔV = −W

4. Write the formula of kinetic energy.

KE = ½mv²

5. Write the speed of a freely falling body from height h.

v = √(2gh)

End of Part 3

Next: Part 4 – Case Study, Match the Columns, Competency-Based Questions & HOTS

CBSE Class 11 Physics

Chapter 5.7 – The Concept of Potential Energy

Part 4 : Case Study, Match the Columns, Competency-Based Questions & HOTS

Section I : Case Study Questions

Case Study

A ball of mass 2 kg is lifted vertically to a height of 10 m. It is then released and falls freely under gravity. Take g = 9.8 m/s². Answer the following questions.

1. What type of energy does the ball possess at the highest point?

Potential Energy.

2. Calculate the gravitational potential energy of the ball.

Given:
Mass = 2 kg
Height = 10 m
g = 9.8 m/s²

PE = mgh
= 2 × 9.8 × 10
= 196 J

Answer: 196 J

3. What happens to the potential energy during free fall?

Potential energy decreases continuously.

4. Which form of energy increases during free fall?

Kinetic Energy.

5. Which law is verified in this example?

Law of Conservation of Mechanical Energy.

Section J : Match the Columns

Column A	Column B
1. Potential Energy	A. Joule
2. Kinetic Energy	B. Energy of Motion
3. Gravity	C. Conservative Force
4. Friction	D. Non-Conservative Force
5. SI Unit of Potential Energy	E. Stored Energy

Correct Matching

Column A	Column B
1	E
2	B
3	C
4	D
5	A

Section K : Competency-Based Questions

1. Why does a book kept on a table possess potential energy?

Because it is at a height above the ground and has the ability to do work if allowed to fall.

2. Why is no work done in moving a body horizontally on a frictionless surface?

Because the height of the body does not change. Therefore, gravitational potential energy remains constant.

3. Why does a stretched spring possess potential energy?

Because energy is stored due to the change in its shape (configuration).

4. Why does an object gain kinetic energy while falling?

Because its gravitational potential energy is converted into kinetic energy during free fall.

5. Why is gravity considered a conservative force?

Because the work done by gravity depends only on the initial and final positions, not on the path followed.

Section L : HOTS (Higher Order Thinking Skills)

1. Can a body have potential energy even when it is at rest? Explain.

Yes. A body at rest can possess potential energy due to its position or configuration. For example, a book placed on a shelf has gravitational potential energy.

2. Why does the speed of a body at the bottom of a smooth inclined plane not depend on the angle of inclination?

Because the loss of potential energy depends only on the vertical height. Hence, the final kinetic energy and speed depend only on height, not on the angle of inclination.

3. Explain why friction cannot store potential energy.

Friction is a non-conservative force. The work done against friction is converted into heat and sound energy instead of being stored as potential energy.

4. A body is lifted to two different heights. At which height will its potential energy be greater? Why?

The potential energy will be greater at the larger height because gravitational potential energy is directly proportional to height (PE = mgh).

5. Give one practical example showing the conversion of potential energy into kinetic energy.

A roller coaster at the top of a track has maximum potential energy. As it moves downward, its potential energy is converted into kinetic energy, increasing its speed.

Section M : Extra Practice Questions

1. State the principle of conservation of mechanical energy.
2. Write any two examples of conservative forces.
3. Write any two examples of non-conservative forces.
4. Explain why potential energy is called stored energy.
5. Write the SI unit and dimensional formula of potential energy.

Answers:

1. Total mechanical energy remains constant when only conservative forces act.
2. Gravitational force and spring force.
3. Frictional force and air resistance.
4. Because it is stored due to position or configuration and can later convert into kinetic energy.
5. SI Unit: Joule (J), Dimensional Formula: [ML²T⁻²]

✅ End of Complete CBSE Class 11 Physics Question Bank
Chapter 5.7 – The Concept of Potential Energy

Includes:

• ✔ MCQs
• ✔ Very Short Answer Questions
• ✔ Short Answer Questions
• ✔ Long Answer Questions
• ✔ Assertion & Reason
• ✔ Fill in the Blanks
• ✔ Statement-Based Questions
• ✔ Case Study Questions
• ✔ Match the Columns
• ✔ Competency-Based Questions
• ✔ HOTS Questions

Work Energy Power Introduction Notes for NEET Physics Beginners

 NEET Physics Work Energy Power Introduction Explained Simply

Simple visual explanation of Work, Energy and Power with real-life examples for NEET Physics beginners.

- Dr.Sanjaykumar Pawar 

Work, Energy and Power – Introduction (NEET Level Easy Notes)

1. Meaning of Work in Daily Life

• In everyday life, the word work is used for any activity that requires effort.
• Examples:
  • A farmer ploughing a field.
  • A construction worker carrying bricks.
  • A student studying for an examination.
  • An artist painting a landscape.
• All these activities are commonly called "work".

Important NEET Point

• The meaning of work in Physics is different from its everyday meaning.
• In Physics, work has a specific and precise definition.

---

2. Meaning of Energy in Daily Life

• A person who can work for many hours is said to have high energy or stamina.
• Long-distance runners are admired for their stamina and energy.
• In daily language, energy means the ability to perform activities without getting tired.

Important NEET Point

• In Physics, energy is defined as the capacity to do work.
• The concept is similar to everyday usage but is defined more accurately.

Key Definition

Energy = Capacity to do work

---

3. Relation Between Work and Energy

• Work and energy are closely related.
• A body must possess energy to perform work.
• If a body has more energy, it can do more work.

Example

• A charged battery can run a fan because it has energy.
• Food provides energy to our body, enabling us to do work.

NEET Formula Concept

• Energy and work have the same SI unit: Joule (J).

---

4. Meaning of Power in Daily Life

• The word power is used in different ways in everyday language.
• In sports like karate or boxing, powerful punches are often discussed.
• Such punches are delivered very quickly and forcefully.

Important Observation

• Here, power is associated with doing something rapidly.

---

5. Meaning of Power in Physics

• In Physics, power is related to how fast work is done.
• It tells us the rate of doing work.

Key Definition

Power = Work done per unit time

Formula

P=\frac{W}{t}

Where:

• = Power
• = Work done
• = Time taken

SI Unit

• Watt (W)

---

6. Difference Between Daily Life and Physics Meanings

Quantity	Everyday Meaning	Physics Meaning
Work	Any effort or activity	Force causing displacement
Energy	Stamina or ability to work	Capacity to do work
Power	Strength or forcefulness	Rate of doing work

NEET Tip

• Everyday meanings and physics definitions are not exactly the same.
• Physics uses precise mathematical definitions.

---

7. Aim of This Chapter

This chapter helps us understand:

1. Work
2. Energy
3. Power

These are three important physical quantities used throughout Physics.

---

8. Mathematical Requirement Before Studying Work

• Before learning work, we need one mathematical concept: Scalar Product (Dot Product) of Two Vectors.

Why?

• The formula of work involves the dot product of force and displacement vectors.

Formula

W = \vec{F}\cdot \vec{s}

Where:

• = Force vector
• = Displacement vector

---

NEET Quick Revision

Definitions

• Work: Energy transferred when a force causes displacement.
• Energy: Capacity to do work.
• Power: Rate of doing work.

Formulas

W = \vec{F}\cdot\vec{s}

P=\frac{W}{t}

SI Units

• Work → Joule (J)
• Energy → Joule (J)
• Power → Watt (W)

One-Line NEET Facts

• Energy is the capacity to do work.
• Power tells how quickly work is done.
• Work, energy, and power have precise scientific meanings.
• Dot product of vectors is required to understand work.
• Work and energy are measured in joules.
• Power is measured in watts.

INTRODUCTION: WORK, ENERGY & POWER

│

├── Work (Everyday Meaning)

│   │

│   ├── Farmer ploughing field

│   ├── Worker carrying bricks

│   ├── Student studying

│   └── Artist painting

│

│   → Any effort or activity is called work

│

├── Work (Physics Meaning)

│   │

│   ├── Has a definite definition

│   └── Different from daily-life meaning

│

├── Energy (Everyday Meaning)

│   │

│   ├── Stamina

│   ├── Ability to work for long hours

│   └── Long-distance runners have high energy

│

├── Energy (Physics Meaning)

│   │

│   ├── Capacity to do work

│   └── Related directly to work

│

├── Relation Between Work & Energy

│   │

│   ├── Energy enables work

│   ├── More energy → More work possible

│   └── Work and energy are closely connected

│

├── Power (Everyday Meaning)

│   │

│   ├── Powerful punches in boxing

│   ├── Powerful kicks in karate

│   └── Associated with speed and strength

│

├── Power (Physics Meaning)

│   │

│   ├── Rate of doing work

│   └── How quickly work is done

│

├── Physics vs Daily Life

│   │

│   ├── Work → Precise scientific meaning

│   ├── Energy → Capacity to do work

│   └── Power → Work done per unit time

│

├── Aim of the Chapter

│   │

│   ├── Understand Work

│   ├── Understand Energy

│   └── Understand Power

│

└── Mathematical Prerequisite

    │

    ├── Scalar Product (Dot Product)

    ├── Product of two vectors

    └── Required for studying Work

NEET KEYWORDS

│

├── Work

├── Energy = Capacity to do Work

├── Power = Work/Time

└── Scalar (Dot) Product of Vectors

Work, Energy and Power (Introduction) – Question Bank (NEET/Foundation Level)

A. Multiple Choice Questions (MCQs)

1. In everyday language, work refers to:

a) Force only
b) Any activity involving effort
c) Energy only
d) Power only

Answer: b) Any activity involving effort

---

2. In Physics, work has:

a) No definition
b) A vague meaning
c) A definite and precise meaning
d) A social meaning

Answer: c) A definite and precise meaning

---

3. Energy is defined as:

a) Capacity to do work
b) Rate of work
c) Force × time
d) Mass × velocity

Answer: a) Capacity to do work

---

4. Power in Physics is related to:

a) Mass
b) Temperature
c) Rate of doing work
d) Momentum

Answer: c) Rate of doing work

---

5. Before studying work, we need to learn:

a) Integration
b) Differentiation
c) Scalar product of vectors
d) Matrices

Answer: c) Scalar product of vectors

---

B. Very Short Answer Questions (1 Mark)

1. What is energy?

Answer: Energy is the capacity to do work.

2. What is power?

Answer: Power is the rate of doing work.

3. What is the SI unit of energy?

Answer: Joule (J).

4. What is the SI unit of power?

Answer: Watt (W).

5. Which mathematical operation is required to study work?

Answer: Scalar (dot) product of vectors.

---

C. Short Answer Questions (2–3 Marks)

1. Why is the physics definition of work different from the everyday definition?

Answer: In everyday life, any effort is called work. In Physics, work is defined precisely and depends on force and displacement. Therefore, not every effort is considered work in Physics.

---

2. How are work and energy related?

Answer: Energy is the capacity to do work. A body possessing energy can perform work. More energy means more ability to do work.

---

3. Explain the meaning of power in Physics.

Answer: Power is the rate at which work is done. It tells us how quickly a task is completed.

Formula: P = W/t

---

D. Long Answer Questions (5 Marks)

1. Explain the terms work, energy and power in daily life and Physics.

Answer:

Work:

• In daily life, any effort is called work.
• In Physics, work has a precise definition involving force and displacement.

Energy:

• In daily life, energy means stamina or strength.
• In Physics, energy is the capacity to do work.

Power:

• In daily life, power refers to strength or forcefulness.
• In Physics, power is the rate of doing work.

These three quantities are closely related because energy enables work and power measures how fast work is done.

---

2. Why is scalar product important in the study of work?

Answer:

Work is calculated using force and displacement vectors.

Formula: W = F · s

The symbol "·" represents the scalar (dot) product. Therefore, understanding scalar product is necessary before studying the concept of work.

---

E. Fill in the Blanks

1. Energy is the _______ to do work. Answer: capacity

2. Power is the _______ of doing work. Answer: rate

3. The SI unit of power is _______. Answer: watt

4. The SI unit of energy is _______. Answer: joule

5. Work in Physics has a _______ definition. Answer: precise

---

F. True/False Statements

1. Every effort in daily life is considered work in Physics. Answer: False

2. Energy is the capacity to do work. Answer: True

3. Power measures how quickly work is done. Answer: True

4. Work and energy are unrelated quantities. Answer: False

5. Scalar product is needed to study work. Answer: True

---

G. Assertion and Reason Questions

1.

Assertion (A): Energy is the capacity to do work.

Reason (R): A body with energy can perform work.

Answer: Both A and R are true, and R is the correct explanation of A.

---

2.

Assertion (A): Power is the rate of doing work.

Reason (R): Power tells how quickly work is completed.

Answer: Both A and R are true, and R is the correct explanation of A.

---

3.

Assertion (A): Every effort is work in Physics.

Reason (R): Physics uses a precise definition of work.

Answer: Assertion is false, Reason is true.

---

4.

Assertion (A): Scalar product is required in the study of work.

Reason (R): Work is defined using force and displacement vectors.

Answer: Both A and R are true, and R is the correct explanation of A.

---

H. Statement-Based Questions

Statement I:

Energy is the capacity to do work.

Statement II:

Power is the rate at which work is done.

Choose the correct option:

a) Both statements are true
b) Statement I true, II false
c) Statement I false, II true
d) Both false

Answer: a) Both statements are true

---

Statement I:

All activities in daily life are work in Physics.

Statement II:

Physics gives a precise definition of work.

Answer: Statement I is false, Statement II is true.

---

I. Case Study Questions

Case Study 1

A student studies for six hours daily. A farmer ploughs the field. A boxer delivers a fast punch.

Answer the following:

1. In everyday language, all these activities are examples of:

a) Energy b) Work c) Force d) Momentum

Answer: b) Work

2. The boxer's fast punch is related to:

a) Mass b) Power c) Temperature d) Density

Answer: b) Power

3. Energy is defined as:

a) Capacity to do work b) Force per unit area c) Rate of change of velocity d) Momentum

Answer: a) Capacity to do work

4. Power tells us:

a) How much mass exists b) How quickly work is done c) How much energy exists d) How much force acts

Answer: b) How quickly work is done

---

J. Match the Columns

Column A	Column B
1. Energy	a. Rate of doing work
2. Power	b. Capacity to do work
3. Work	c. Precise physics definition
4. Scalar Product	d. Mathematical prerequisite

Answers

1 → b

2 → a

3 → c

4 → d

---

K. HOTS (Higher Order Thinking Skills)

1. Can a person feel tired and still do zero work in Physics?

Answer: Yes. A person may apply effort and become tired, but if there is no displacement in the direction of force, the work done in Physics can be zero.

---

2. Why are work and energy measured in the same unit?

Answer: Energy is the capacity to do work. Since both are closely related and represent the same quantity in different forms, they have the same SI unit, Joule (J).

INTERNAL LINKS 

/neet-physics-work-energy-power-notes

/class-11-physics-work-energy-chapter

/physics-formulas-work-energy-power

/neet-physics-important-definitions

/scalar-product-dot-product-explained

/physics-basic-concepts-for-beginners