Conservation of Mechanical Energy Class 11 Notes, MCQs, Questions & Answers | CBSE & NEET

-  Dr Sanjay Kumar Pawar 

Conservation of Mechanical Energy Class 11 Physics Notes PDF | CBSE & NEET 

Conservation of Mechanical Energy explained with a falling ball showing the conversion of potential energy into kinetic energy.

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Link this page to related Class 11 Physics topics to improve SEO and user navigation:

1. Work, Energy and Power Class 11 Notes
2. Work-Energy Theorem Explained
3. Potential Energy Class 11 Notes
4. Kinetic Energy Formula and Examples
5. Conservative and Non-Conservative Forces
6. Gravitational Potential Energy Notes
7. Free Fall Motion Class 11
8. Laws of Motion Class 11
9. Newton's Laws of Motion Notes
10. Circular Motion Class 11 Notes
11. System of Particles and Rotational Motion
12. Gravitation Class 11 Notes
13. Mechanical Properties of Solids
14. Complete Class 11 Physics Notes Index 
15. Class 11 Physics MCQs with Answers
16. CBSE Class 11 Physics Important Questions
17. NEET Physics Chapter-wise Notes
18. NCERT Solutions for Class 11 Physics
19. Class 11 Physics Formula Sheet
20. Previous Year CBSE Class 11 Physics Questions

Chapter 5.8
Conservation of Mechanical Energy

Definition:
Mechanical Energy is the sum of Kinetic Energy (KE) and Potential Energy (PE).

Mechanical Energy = KE + PE

1. Work-Energy Theorem

Suppose a body moves through a small distance Δx under the action of force F. According to the Work-Energy Theorem,

ΔK = F(x) Δx

This means the work done by a force changes the kinetic energy of the body.

• Positive work increases kinetic energy.
• Negative work decreases kinetic energy.

2. Conservative Force

If the force is conservative, then potential energy can be defined.

−ΔU = F(x) Δx

The negative sign shows that whenever potential energy decreases, kinetic energy increases.

Example:
A falling stone loses potential energy and gains kinetic energy.

3. Combining the Equations

From the two equations:

ΔK = −ΔU

Therefore,

ΔK + ΔU = 0

or

Δ(K + U) = 0

4. Conservation of Mechanical Energy

Since Δ(K+U)=0, the total mechanical energy never changes.

K + U = Constant

This is called the Law of Conservation of Mechanical Energy.

5. Equation Between Two Positions

Ki + Ui = Kf + Uf

The total mechanical energy before motion equals the total mechanical energy after motion.

6. Conservative Force - Important Properties

• Potential energy can be defined.
• Work depends only on initial and final positions.
• Work does not depend on the path.
• Work done in a closed path is zero.
• Mechanical energy remains conserved.

7. Example - Falling Ball

A ball of mass m is dropped from height H. Initially the velocity is zero.

At Height H

PE = mgH

KE = 0

EH = mgH

At Height h

PE = mgh

KE = ½mv²h

Eh = mgh + ½mv²h

At Ground Level

PE = 0

KE = ½mv²f

E0 = ½mv²f

8. Conservation of Energy

EH = Eh = E0

Since only gravity acts on the body, mechanical energy remains constant.

mgH = mgh + ½mv²h = ½mv²f

9. Final Velocity

Using conservation of energy,

mgH = ½mv²f

After simplifying,

vf = √(2gH)

10. Velocity at Height h

mgH = mgh + ½mv²h

Therefore,

vh² = 2g(H − h)

11. Energy Conversion

Position	Potential Energy	Kinetic Energy
Top	Maximum	Zero
Middle	Decreasing	Increasing
Ground	Zero	Maximum

12. Important Points for NEET

• Mechanical Energy = KE + PE
• Gravity is a conservative force.
• Spring force is also conservative.
• Mechanical energy remains constant if only conservative forces act.
• Work done by a conservative force depends only on the initial and final positions.
• Work done in a closed path is zero.
• At the highest point, PE is maximum and KE is zero.
• At the ground, KE is maximum and PE is zero.
• Potential energy converts into kinetic energy during free fall.

13. Formula Sheet

Mechanical Energy = KE + PE

ΔK + ΔU = 0

K + U = Constant

Ki + Ui = Kf + Uf

PE = mgh

KE = ½mv²

vf = √(2gH)

vh² = 2g(H − h)

Work done in a Closed Path = 0

Prepared for NEET Physics Students • Chapter 5.8 - Conservation of Mechanical Energy

Conservation of Mechanical Energy

What is Mechanical Energy?

Mechanical Energy is the sum of Kinetic Energy (KE) and Potential Energy (PE).

Mechanical Energy = KE + PE

Work-Energy Theorem

When a force acts on an object, its kinetic energy changes.

ΔKE = Work Done

For conservative forces, Potential Energy decreases when Kinetic Energy increases.

ΔKE + ΔPE = 0

Energy Conversion During Falling

Top
PE Maximum
KE Zero

Middle
PE ↓
KE ↑

Ground
PE Zero
KE Maximum

Visual Falling Ball

⬇

As the ball falls, Potential Energy continuously converts into Kinetic Energy.

Example

Position	Potential Energy	Kinetic Energy	Total Energy
Top	100 J	0 J	100 J
Middle	60 J	40 J	100 J
Ground	0 J	100 J	100 J

Important Formulae

PE = mgh

KE = ½mv²

KE + PE = Constant

vf = √(2gH)

vh² = 2g(H − h)

NEET Remember:

• Gravity is a conservative force.
• Total Mechanical Energy remains constant if only conservative forces act.
• At the highest point: PE is maximum and KE is zero.
• At the ground: KE is maximum and PE is zero.
• Potential Energy converts into Kinetic Energy during falling.

CBSE Class 11 Physics

Chapter 5.8 - Conservation of Mechanical Energy

Question Bank with Answers

---

Part A - Multiple Choice Questions

1. Mechanical energy is the sum of

1. Potential energy and Heat energy
2. Kinetic energy and Potential energy
3. Heat energy and Electrical energy
4. Sound energy and Potential energy

Answer: B

2. Mechanical energy remains constant when

1. Friction acts
2. Air resistance acts
3. Only conservative forces act
4. External force acts

Answer: C

3. Which one is a conservative force?

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

Answer: B

4. Work done by a conservative force depends on

1. Path followed
2. Distance travelled
3. Initial and final positions only
4. Speed

Answer: C

5. Work done in a closed path by gravity is

1. Positive
2. Negative
3. Zero
4. Infinite

Answer: C

---

Part B - Very Short Answer Questions

1. Define mechanical energy.

Answer: Mechanical energy is the sum of kinetic energy and potential energy.

2. Write the formula of mechanical energy.

Answer: E = KE + PE

3. Name one conservative force.

Answer: Gravitational force.

4. Write the formula of kinetic energy.

Answer: KE = ½mv²

5. Write the formula of potential energy.

Answer: PE = mgh

---

Part C - Short Answer Questions

1. What is conservation of mechanical energy?

Answer:
When only conservative forces act on a body, the total mechanical energy (kinetic energy + potential energy) remains constant throughout the motion.

2. What is a conservative force?

Answer:
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

---

Part D - Long Answer Questions

1. State the law of conservation of mechanical energy.

Answer:
If only conservative forces act on a body, its total mechanical energy remains constant. Mechanical Energy = Kinetic Energy + Potential Energy Initial Energy Ki + Ui Final Energy Kf + Uf Therefore, Ki + Ui = Kf + Uf Example: A freely falling body loses potential energy and gains kinetic energy. The total mechanical energy remains constant.

---

Part E - Assertion and Reason

Assertion: Mechanical energy remains constant when only conservative forces act.

Reason: Gravity is a conservative force.

Answer: Both Assertion and Reason are true, and Reason is the correct explanation.

---

Part F - Fill in the Blanks

1. Mechanical energy is the sum of ______ and ______.
2. Gravity is a ______ force.
3. Potential energy converts into ______ during free fall.
4. Work done in a closed path is ______.
5. Mechanical energy remains ______ when only conservative forces act.

Answers:

1. Kinetic energy, Potential energy
2. Conservative
3. Kinetic energy
4. Zero
5. Constant

---

Part G - Match the Columns

Column A	Column B
Gravity	Conservative force
Friction	Non-conservative force
Potential Energy	mgh
Kinetic Energy	½mv²

Matching Answers 1 → Conservative force 2 → Non-conservative force 3 → mgh 4 → ½mv²

---

Part H - Case Study

A ball of mass 2 kg is dropped from a height of 20 m. Ignore air resistance.

Q1. Which energy is maximum at the top?

Answer: Potential Energy

Q2. Which energy is maximum at the ground?

Answer: Kinetic Energy

Q3. Calculate total mechanical energy at the top. Take g = 10 m/s².

PE = mgh = 2 × 10 × 20 = 400 J Answer = 400 Joule

Q4. Is mechanical energy conserved?

Yes. Only gravity acts.

---

Important Formulae

• E = KE + PE
• KE = ½mv²
• PE = mgh
• Ki + Ui = Kf + Uf
• Δ(KE + PE) = 0
• v = √(2gH)
• v² = 2g(H − h)
• Work in closed path = 0

---

End of CBSE Class 11 Physics Question Bank

Work, Energy and Power Notes for NEET: Kinetic Energy & Variable Force

-  Dr.Sanjaykumar Pawar 

Kinetic Energy and Work Done by Variable Force explained with formulas, examples, and graphical interpretation for NEET aspirants.

INTERNAL LINK SUGGESTIONS

6. Laws of Motion Complete Notes

7. Motion in One Dimension Notes

8. Motion in a Plane Notes

9. Work Energy Theorem Explained

10. Potential Energy Notes

11. Conservation of Energy Notes

12. Power Formula and Applications

13. Mechanical Energy Examples

14. NCERT Physics Class 11 Solutions

15. NEET Physics Formula Sheet

16. Rotational Motion Notes

17. Gravitation Complete Notes

18. Oscillations and SHM Notes

19. Units and Measurements Notes

20. NEET Physics MCQs with Answers 

FAQ QUESTIONS

Q1. What is kinetic energy?

A. Kinetic energy is the energy possessed by a body due to its motion.

Q2. What is the formula of kinetic energy?

A. K = 1/2 mv².

Q3. What is work done by a variable force?

A. Work done by a variable force equals the area under the force-displacement graph.

Q4. Why is speed not reduced by 90% when kinetic energy becomes 10%?

A. Because kinetic energy is proportional to the square of speed.

Q5. What is the SI unit of work?

A. Joule (J).

WORK, ENERGY AND POWER

1. Kinetic Energy (K)

Kinetic energy is the energy possessed by a body due to its motion.

K = ½ mv²

Where:

• m = mass of the object
• v = speed of the object
• K = kinetic energy

2. Typical Kinetic Energies

Object	Mass (kg)	Speed (m/s)	Kinetic Energy (J)
Car	2000	25	6.3 × 10⁵
Running Athlete	70	10	3.5 × 10³
Bullet	0.05	200	10³
Stone Dropped from 10 m	-	14	10²
Rain Drop	3.5 × 10⁻⁵	9	1.4 × 10⁻³
Air Molecule	≈ 10⁻²⁶	500	≈ 10⁻²¹

Heavy objects moving fast possess very large kinetic energy.

3. Example: Bullet Passing Through Plywood

Given:

• Mass of bullet = 50 g = 0.05 kg
• Initial speed = 200 m/s
• Final kinetic energy = 10% of initial kinetic energy

Step 1: Initial Kinetic Energy

Ki = ½mv²

Ki = ½ × 0.05 × (200)²

Ki = 1000 J

Step 2: Final Kinetic Energy

Kf = 10% of 1000

Kf = 100 J

Step 3: Calculate Final Speed

½mvf² = 100

vf = √(2 × 100 / 0.05)

vf = 63.2 m/s

Answer: Emergent speed = 63.2 m/s

4. Important Concept for NEET

Kinetic Energy is proportional to the square of speed.

K ∝ v²

If kinetic energy becomes 10%:

vf = √0.1 × vi

vf = 0.316 × vi

Speed becomes 31.6% of original speed.

Reduction in speed:

100 − 31.6 = 68.4%

Speed is reduced by approximately 68%, not 90%.

5. Work Done by a Variable Force

Constant Force

A constant force is a force whose magnitude and direction remain unchanged.

Examples:

• Weight of a body near Earth
• Pushing a box with constant force

W = F × s

Where:

• W = Work Done
• F = Force
• s = Displacement

Variable Force

A variable force changes with position, time, or direction.

Examples:

• Spring Force
• Gravitational Force
• Electric Force

For variable force, W = Fs cannot be directly used.

6. Small Displacement Method

Consider a very small displacement Δx.

Over this tiny distance, force can be treated as constant.

ΔW = F(x)Δx

Where:

• ΔW = Small work done
• F(x) = Force at position x
• Δx = Small displacement

7. Total Work Done

Adding work done over many small intervals:

W = Σ F(x)Δx

This is called summation.

Meaning:

• Divide motion into many small parts.
• Find work done in each part.
• Add all the small works.

8. Graphical Interpretation

In a Force vs Position graph:

• Y-axis → Force F(x)
• X-axis → Position x

Area of one small rectangle:

ΔA = F(x)Δx

Since:

ΔW = F(x)Δx

Therefore:

ΔW = ΔA

Small Work Done = Area of Small Rectangle

9. Integral Form of Work Done

When Δx becomes extremely small:

W = ∫ F(x) dx

Limits:

W = ∫_xi^xf F(x) dx

Where:

• xi = Initial Position
• xf = Final Position

Work Done by Variable Force = Area Under Force-Position Curve

10. NEET Quick Revision

Kinetic Energy

K = ½mv²

• KE ∝ Mass
• KE ∝ Speed²

If Speed Doubles

K → 4K

If Speed Triples

K → 9K

Variable Force

ΔW = F(x)Δx

W = ΣF(x)Δx

W = ∫F(x)dx

Most Important NEET Statement

✔ Work Done = Area under Force-Displacement Graph

Frequently Asked Relation

If KE becomes n times:

v = √n × Initial Speed

If speed becomes n times:

K = n² × Initial Kinetic Energy

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CBSE Class 11 Physics Question Bank

Chapter: Work, Energy and Power

Section A: Very Short Answer Questions (1 Mark)

1. Define kinetic energy.

Kinetic energy is the energy possessed by a body due to its motion.

2. Write the SI unit of kinetic energy.

Joule (J)

3. Write the formula for kinetic energy.

K = ½mv²

4. On what factors does kinetic energy depend?

Mass and square of velocity.

5. What is the kinetic energy of a body at rest?

Zero.

6. What is a variable force?

A force whose magnitude changes with position is called a variable force.

7. Write the expression for small work done by a variable force.

ΔW = F(x)Δx

8. What does the area under an F-x graph represent?

Work done by the force.

9. What is the SI unit of work?

Joule (J)

10. Write the integral form of work done.

W = ∫F(x)dx

Section B: Short Answer Questions (2 Marks)

1. Why does a bullet possess large kinetic energy despite having small mass?

A bullet has very high speed. Since kinetic energy depends on the square of velocity, it possesses large kinetic energy.

2. Calculate the kinetic energy of a body of mass 4 kg moving with speed 5 m/s.

K = ½mv²
= ½ × 4 × 25
= 50 J

3. Distinguish between constant force and variable force.

Constant Force	Variable Force
Remains unchanged	Changes with position
W = Fs	W = ∫Fdx
Example: Weight	Example: Spring Force

4. State the graphical interpretation of work done.

Work done by a force is equal to the area under the force-displacement graph.

5. If velocity doubles, how does kinetic energy change?

K ∝ v²
Therefore kinetic energy becomes four times.

Section C: Long Answer Questions (5 Marks)

1. Derive the expression for kinetic energy.

Work done W = Fs

Using F = ma
W = mas

Using equation of motion:
v² − u² = 2as
a = (v² − u²)/2s

Substituting:
W = m(v² − u²)/2

For u = 0:
K = ½mv²

2. Explain work done by a variable force with graphical interpretation.

For a small displacement Δx:
ΔW = F(x)Δx

Adding all small works:
W = ΣF(x)Δx

As Δx approaches zero:
W = ∫F(x)dx

Thus, work done by a variable force equals the area under the force-displacement graph.

Section D: Multiple Choice Questions

1. Kinetic energy depends on:

• A. Mass only
• B. Velocity only
• C. Mass and velocity
• D. Mass and square of velocity

Answer: D

2. SI unit of kinetic energy is:

• A. Newton
• B. Joule
• C. Watt
• D. Pascal

Answer: B

3. If speed triples, kinetic energy becomes:

• A. 3 times
• B. 6 times
• C. 9 times
• D. 27 times

Answer: C

4. Area under force-displacement graph represents:

• A. Velocity
• B. Momentum
• C. Work done
• D. Acceleration

Answer: C

Section E: Assertion and Reason

Assertion (A): Kinetic energy is proportional to square of velocity.
Reason (R): K = ½mv².

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

Assertion (A): Area under force-displacement graph gives work done.
Reason (R): ΔW = FΔx.

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

Section F: Fill in the Blanks

1. Kinetic energy is measured in Joule.
2. The formula of kinetic energy is ½mv².
3. Work done by variable force equals the area under F-x graph.
4. Kinetic energy is proportional to the square of velocity.
5. The SI unit of work is Joule.

Section G: Match the Columns

Column A	Column B
Kinetic Energy	Energy due to motion
Joule	Unit of work
Variable Force	Spring force
Area under F-x graph	Work done

Correct Matching:
A → Energy due to motion
B → Unit of work
C → Spring force
D → Work done

Section H: Statement Based Questions

Statement I: A bullet moving at high speed possesses kinetic energy.
Statement II: Kinetic energy depends on square of velocity.

Both statements are true.

Section I: Case Study Questions

A bullet of mass 0.05 kg is fired with speed 200 m/s. After passing through a wooden block, it retains only 10% of its original kinetic energy.

1. What is the initial kinetic energy?

1000 J

2. What is the final kinetic energy?

100 J

3. What is the final speed?

63.2 m/s

4. Is speed reduced by 90%?

No.

5. Why?

Because kinetic energy is proportional to velocity squared.

Section J: Competency Based Questions

1. A car moving at 20 m/s has kinetic energy K. If its speed becomes 40 m/s, what will be its kinetic energy?

K' = (40/20)² K = 4K

2. Why does a fast-moving cricket ball hurt more than a slow-moving ball?

A fast-moving ball possesses greater kinetic energy because kinetic energy depends on the square of speed.

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Work and Kinetic Energy Explained: Work-Energy Theorem for NEET

- Dr.Sanjaykumar Pawar 

Work-Energy Theorem showing how work done by a force changes the kinetic energy of an object.

Work-Energy Theorem Notes for NEET |

Kinetic Energy Made Easy

NOTIONS OF WORK AND KINETIC ENERGY

│

├── 1. Kinematics Relation

│   │

│   ├── Equation

│   │   └── v² − u² = 2as

│   │

│   ├── u = Initial Velocity

│   ├── v = Final Velocity

│   ├── a = Acceleration

│   └── s = Displacement

│

├── 2. Multiply by m/2

│   │

│   ├── (m/2)(v² − u²) = (m/2)(2as)

│   │

│   ├── ½mv² − ½mu² = mas

│   │

│   ├── Newton's Second Law

│   │   └── F = ma

│   │

│   └── Therefore

│       └── ½mv² − ½mu² = Fs

│

├── 3. Three-Dimensional Form

│   │

│   ├── v² − u² = 2(a·d)

│   │

│   ├── a = Acceleration Vector

│   ├── d = Displacement Vector

│   └── a·d = Dot Product

│

├── 4. Kinetic Energy (K)

│   │

│   ├── Formula

│   │   └── K = ½mv²

│   │

│   ├── Definition

│   │   └── Energy due to motion

│   │

│   ├── Unit

│   │   └── Joule (J)

│   │

│   └── Properties

│       ├── Always Positive

│       ├── Depends on Mass

│       └── Depends on Velocity²

│

├── 5. Work Done (W)

│   │

│   ├── Formula

│   │   └── W = F·d

│   │

│   ├── General Formula

│   │   └── W = Fd cosθ

│   │

│   ├── Definition

│   │   └── Force × Displacement

│   │

│   └── Unit

│       └── Joule (J)

│

├── 6. Work-Energy Equation

│   │

│   ├── Initial Kinetic Energy

│   │   └── Ki = ½mu²

│   │

│   ├── Final Kinetic Energy

│   │   └── Kf = ½mv²

│   │

│   └── Relation

│       └── Kf − Ki = W

│

├── 7. Work-Energy Theorem

│   │

│   ├── Statement

│   │   └── Change in Kinetic Energy

│   │       = Net Work Done

│   │

│   ├── Formula

│   │   └── Wnet = ΔK

│   │

│   └── Alternative Form

│       └── Wnet = Kf − Ki

│

├── 8. Types of Work

│   │

│   ├── Positive Work

│   │   ├── W > 0

│   │   ├── Force along Motion

│   │   └── Kinetic Energy Increases

│   │

│   ├── Negative Work

│   │   ├── W < 0

│   │   ├── Force opposite Motion

│   │   └── Kinetic Energy Decreases

│   │

│   └── Zero Work

│       ├── W = 0

│       ├── Force ⟂ Displacement

│       └── Kinetic Energy Constant

│

└── 9. NEET Formula Box

    │

    ├── K = ½mv²

    ├── W = Fd cosθ

    ├── W = F·d

    ├── Wnet = ΔK

    └── Wnet = Kf − Ki

FINAL CONCEPT

│

└── Net Work Done on a Body

    └── Produces Equal Change in Kinetic Energy

        └── Wnet = ΔK 

CBSE Class 11 Physics

Work, Energy and Power

Topic: Notions of Work and Kinetic Energy – Work-Energy Theorem

---

A. Multiple Choice Questions (MCQs)

1. The kinetic energy of a body is given by:

(a) mv² (b) ½mv² (c) mv (d) m²v

Answer: (b) ½mv²

---

2. SI unit of work is:

(a) Newton (b) Watt (c) Joule (d) Pascal

Answer: (c) Joule

---

3. Work done is maximum when angle between force and displacement is:

(a) 0° (b) 45° (c) 90° (d) 180°

Answer: (a) 0°

---

4. If force is perpendicular to displacement, work done is:

(a) Positive (b) Negative (c) Zero (d) Infinite

Answer: (c) Zero

---

5. Work-Energy theorem states:

(a) Work done equals momentum (b) Work done equals force (c) Work done equals change in kinetic energy (d) Work done equals acceleration

Answer: (c)

---

6. Kinetic energy depends on:

(a) Mass only (b) Velocity only (c) Mass and velocity (d) Density

Answer: (c)

---

7. If velocity becomes twice, kinetic energy becomes:

(a) Two times (b) Four times (c) Six times (d) Eight times

Answer: (b)

---

8. The dimension of work and energy is:

(a) MLT⁻¹ (b) ML²T⁻² (c) ML²T⁻¹ (d) MLT⁻²

Answer: (b)

---

9. Negative work is done when:

(a) Force and displacement are same (b) Force is perpendicular (c) Force opposes displacement (d) Force is zero

Answer: (c)

---

10. The unit of kinetic energy is:

(a) Newton (b) Joule (c) Watt (d) kg

Answer: (b)

---

B. Very Short Answer Questions (1 Mark)

Q1. Define kinetic energy.

Answer: Kinetic energy is the energy possessed by a body due to its motion.

---

Q2. Write the formula of kinetic energy.

Answer: K = ½mv²

---

Q3. State SI unit of work.

Answer: Joule (J)

---

Q4. What is the work done when force is perpendicular to displacement?

Answer: Zero.

---

Q5. State Work-Energy theorem.

Answer: Change in kinetic energy equals the net work done on a body.

---

C. Short Answer Questions (2–3 Marks)

Q1. Define work done. Write its mathematical expression.

Answer:

Work done is the product of force and displacement in the direction of force.

W = Fd cosθ

where θ is the angle between force and displacement.

---

Q2. Why is kinetic energy always positive?

Answer:

K = ½mv²

Since mass is positive and square of velocity is always positive, kinetic energy is always positive.

---

Q3. Distinguish between positive and negative work.

Positive Work	Negative Work
Force acts along displacement	Force acts opposite displacement
Energy increases	Energy decreases
Example: Pulling a cart	Example: Braking a bicycle

---

Q4. Write any two applications of Work-Energy theorem.

Answer:

1. Finding velocity without using time.
2. Calculating work done by forces.

---

D. Long Answer Questions (5 Marks)

Q1. Derive Work-Energy theorem.

Answer:

From equation of motion:

v² − u² = 2as

Multiplying both sides by m/2,

½m(v² − u²) = mas

Since,

F = ma

Therefore,

½mv² − ½mu² = Fs

Now,

Kf = ½mv²

Ki = ½mu²

Thus,

Kf − Ki = W

Hence,

W = ΔK

This proves that net work done on a particle equals change in its kinetic energy.

---

Q2. Explain positive, negative and zero work with examples.

Answer:

1. Positive Work:

   • Force and displacement in same direction.
   • Example: Pulling a trolley.

2. Negative Work:

   • Force opposite displacement.
   • Example: Brakes on bicycle.

3. Zero Work:

   • Force perpendicular to displacement.
   • Example: Centripetal force in circular motion.

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E. Assertion and Reason Questions

Q1.

Assertion (A): Kinetic energy is always positive.

Reason (R): Kinetic energy depends on square of velocity.

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

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Q2.

Assertion (A): Work done by centripetal force is zero.

Reason (R): Centripetal force is perpendicular to displacement.

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

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Q3.

Assertion (A): Negative work increases kinetic energy.

Reason (R): Negative work opposes motion.

Answer: Assertion is false but Reason is true.

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Q4.

Assertion (A): SI unit of work and energy is same.

Reason (R): Both are measured in Joules.

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

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F. Fill in the Blanks

1. Kinetic energy of a body is ______ due to its motion.

Answer: energy

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2. Formula of kinetic energy is ______.

Answer: ½mv²

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3. SI unit of work is ______.

Answer: Joule

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4. Work done is zero when force is ______ to displacement.

Answer: perpendicular

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5. According to Work-Energy theorem,

W = ______

Answer: ΔK

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G. Statement Based Questions

State whether True or False.

1. Kinetic energy can be negative.

Answer: False

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2. Work and energy have same units.

Answer: True

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3. Work done is maximum when θ = 90°.

Answer: False

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4. Work-Energy theorem relates work and kinetic energy.

Answer: True

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5. Negative work decreases kinetic energy.

Answer: True

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H. Match the Columns

Column A

A. Kinetic Energy

B. Work Done

C. Positive Work

D. Negative Work

E. SI Unit

Column B

1. Joule

2. ½mv²

3. Force opposite displacement

4. Fd cosθ

5. Force along displacement

Answers

A → 2

B → 4

C → 5

D → 3

E → 1

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I. Case Study Questions

Case Study

A student pushes a 5 kg box along a horizontal floor with a force of 20 N. The box moves 4 m in the direction of force.

Q1. What is the work done?

W = Fd

= 20 × 4

= 80 J

Answer: 80 J

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Q2. If all work converts into kinetic energy, what is change in kinetic energy?

Answer: 80 J

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Q3. Which theorem relates work and kinetic energy?

Answer: Work-Energy theorem.

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Q4. Is the work positive or negative?

Answer: Positive.

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Q5. Why?

Answer: Force and displacement are in the same direction.

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J. Important Board Exam Questions

1. Define kinetic energy.
2. State and prove Work-Energy theorem.
3. Write SI unit of work and energy.
4. Differentiate positive and negative work.
5. Explain zero work with example.
6. Define work done and derive its expression.
7. Explain Work-Energy theorem with suitable example.
8. Why is kinetic energy always positive?
9. Give practical applications of Work-Energy theorem.
10. Derive K = ½mv² from Work-Energy theorem.

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One-Line Revision

• K = ½mv²

• W = Fd cosθ

• Wnet = ΔK

• Positive Work → KE increases

• Negative Work → KE decreases

• Zero Work → KE remains constant

• SI Unit of Work & Energy = Joule (J)

• Work-Energy Theorem: Net work done = Change in kinetic energy 

Internal Links

Laws of Motion Explained for NEET

Work, Energy and Power Complete Notes

Conservation of Mechanical Energy

Motion in a Straight Line Notes

Motion in a Plane and Vectors

Newton's Laws of Motion Questions

Circular Motion for NEET

Units and Dimensions Physics Notes

Kinematics Formula Sheet

NEET Physics Chapter-wise Revision Notes

NOTIONS OF WORK AND KINETIC ENERGY
THE WORK–ENERGY THEOREM

1. Equation from Kinematics

For rectilinear motion under constant acceleration:

v² − u² = 2as

Where:

• u = Initial velocity
• v = Final velocity
• a = Acceleration
• s = Displacement

This equation relates velocity, acceleration and displacement.

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2. Multiplying by m/2

Multiply both sides by m/2:

(m/2)(v² − u²) = (m/2)(2as)

½mv² − ½mu² = mas

From Newton's Second Law:

F = ma

Therefore:

½mv² − ½mu² = Fs

Important: The left side involves mass and velocity, while the right side involves force and displacement.

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3. Generalisation to Three Dimensions

For motion in three dimensions, vectors are used.

v² − u² = 2(a · d)

Where:

• a = Acceleration vector
• d = Displacement vector
• · = Dot product

Multiplying by m/2:

½mv² − ½mu² = m(a · d)

Since:

F = ma

We get:

½mv² − ½mu² = F · d

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4. Kinetic Energy (K)

The quantity

K = ½mv²

is called Kinetic Energy.

Definition

Kinetic Energy is the energy possessed by a body due to its motion.

SI Unit

Joule (J)

Important Facts

• Kinetic energy is always positive.
• It depends on mass and velocity.
• If velocity doubles, kinetic energy becomes four times.
• If velocity becomes three times, kinetic energy becomes nine times.

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5. Work Done (W)

The quantity

W = F · d

is called Work Done.

Definition

Work is said to be done when a force produces displacement in an object.

Formula

W = Fd cosθ

Where:

• F = Force
• d = Displacement
• θ = Angle between force and displacement

SI Unit

Joule (J)

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6. Work-Energy Equation

Initial kinetic energy:

Ki = ½mu²

Final kinetic energy:

Kf = ½mv²

Substituting in the equation:

Kf − Ki = W

Change in Kinetic Energy = Work Done

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7. Work-Energy Theorem

Statement

The change in kinetic energy of a particle is equal to the work done on it by the net force acting on it.

Mathematically:

Wnet = ΔK

or

Wnet = Kf − Ki

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8. Physical Meaning of Work-Energy Theorem

Case 1: Positive Work

W > 0

Force acts in the direction of motion.

Kf > Ki

Result: Speed increases.

Example: Pushing a moving cart.

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Case 2: Negative Work

W < 0

Force acts opposite to the direction of motion.

Kf < Ki

Result: Speed decreases.

Example: Applying brakes on a bicycle.

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Case 3: Zero Work

W = 0

Force acts perpendicular to displacement.

Kf = Ki

Result: No change in speed.

Example: Centripetal force in circular motion.

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9. Quick NEET Revision Box

Kinetic Energy

K = ½mv²

Work Done

W = Fd cosθ

Work-Energy Theorem

Wnet = Kf − Ki = ΔK

SI Unit

• Work → Joule (J)
• Kinetic Energy → Joule (J)

Key Idea

Net work done on a body changes its kinetic energy.

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NEET One-Line Summary

Whenever a net force does work on an object, its kinetic energy changes by exactly the same amount.

Wnet = ΔK

Prepared for NEET Physics Revision