Work Energy and Power Notes for Competitive Exams – MCQs for UPSC, SSC, Railway, NEET.

Work, Energy and Power

 

Introduction

Work, Energy and Power is one of the highest scoring chapters in Physics for competitive exams like UPSC Prelims, SSC CGL/CHSL, RRB NTPC/Group D, Delhi Police, State PCS and other government exams. Every year, exam papers feature 3–6 direct questions from this topic in the General Science section, making it a must-master chapter for all aspirants.

In simple terms:

·       Work = Force × Distance (when force and motion are in same direction)

·       Energy = Capacity to do work (Kinetic + Potential)

·       Power = Rate of doing work (Work/Time)

This blog explains all key formulas (W = F×d×cosθ, KE = ½mv², PE = mgh, P = W/t), conservation of energy, work-energy theorem and numerical examples in very simple English suitable for non-science background students. No advanced mathematics — just exam-ready concepts, solved problems, common mistakes and PYQ patterns that will help you score full marks in this chapter.

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WORK

Definition: Work is done when a force causes displacement in the direction of force.

Work Done Formula:

W = F × d × cosθ

Where:

W = Work (Joules)

F = Force (Newton)

d = Displacement (meter)

θ = Angle between force and displacement

 

Units of Work:

Unit	Full Form	Equivalent
Joule (J)	Newton-meter (N-m)	kg-m²/s²
Erg	dyne-cm	10⁻⁷ J
kWh	kilowatt-hour	3.6 × 10⁶ J

Special Cases:

θ = 0° → cos0° = 1 → W = F × d (Maximum work)

θ = 90° → cos90° = 0 → W = 0 (No work)

θ = 180° → cos180° = -1 → W = -F × d (Negative work)

 

Types of Work

 

Type	Condition	Example
Positive Work	θ < 90° (cosθ > 0)	Lifting a book (F and d same direction)
Negative Work	θ > 90° (cosθ < 0)	Friction opposing motion
Zero Work	θ = 90° (cosθ = 0)	Satellite orbiting Earth (F ⊥ d)
Variable Force	F changes with distance	Spring: W = ½kx²

Exam Tip: Questions on zero work (gravity on horizontal motion, centripetal force) are very common.

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 ENERGY

 

Definition: Energy is the capacity to do work.

Types of Energy:

Mechanical Energy	Non-Mechanical Energy
Kinetic Energy (motion)	Heat energy
Potential Energy (position)	Chemical energy
Elastic Potential Energy	Electrical energy
Gravitational PE	Nuclear energy
Sound energy	Light energy

 

Law of Conservation of Energy: Energy can neither be created nor destroyed, only transformed from one form to another.

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Work-Energy Theorem

Work-Energy Theorem: The net work done on an object equals the change in its kinetic energy.

W_net = ΔKE = KE_final - KE_initial

W_net = ½mv₂² - ½mv₁²

Proof (for exams):

Work = F × d × cosθ

F = ma → W = ma × d

From equations of motion: v² = u² + 2as

→ W = m × (v² - u²)/2 = ½mv² - ½mu² = ΔKE ✓

Applications:

·       Braking car: Negative work by friction → KE decreases → Car stops

·       Rocket launch: Engines do positive work → KE increases

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Kinetic Energy and Potential Energy

Kinetic Energy (KE):

KE = ½mv²

Where: m = mass (kg), v = velocity (m/s)

Potential Energy (PE):

PE = mgh (Gravitational)

PE = ½kx² (Spring/Elastic)

Where: m = mass, g = 9.8 m/s², h = height

k = spring constant, x = compression

Total Mechanical Energy:

E_total = KE + PE = Constant (if no friction)

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Conservation of Mechanical Energy

Principle: In a closed system with no friction, total mechanical energy remains constant.

KE_initial + PE_initial = KE_final + PE_final

½mv₁² + mgh₁ = ½mv₂² + mgh₂

Solved Example (Exam Type):

A 2 kg ball is dropped from 10m height. Find velocity just before hitting ground.

PE_initial = mgh = 2 × 10 × 10 = 200 J

KE_final = PE_initial = 200 J

½ × 2 × v² = 200 → v² = 200 → v = √200 = 14.14 m/s

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POWER

Definition: Power is the rate of doing work.

Power Formulas:

P = W/t = F × v (when F and v parallel)

P = τ × ω (rotational power)

Units of Power:

Unit	Full Form	Equivalent
Watt (W)	Joule/second (J/s)	1 W = 1 J/s
Horsepower (HP)	-	1 HP = 746 W
kW	kilowatt	1000 W

 

Commercial Unit: 1 kWh = 3.6 × 10⁶ J (electricity bill unit)

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Important Formulas Table (Exam Ready)

 

Concept	Formula	Units
Work	W = F × d × cosθ	Joule (J)
Kinetic Energy	KE = ½mv²	Joule (J)
Gravitational PE	PE = mgh	Joule (J)
Power	P = W/t = F × v	Watt (W)
Work-Energy Theorem	W_net = ΔKE	Joule (J)
Conservation	KE₁ + PE₁ = KE₂ + PE₂	Joule (J)
1 kWh	3.6 × 10⁶ J	Energy

 

Memorise: Work = Energy, Power = Work/Time

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MCQs 

Q1. Work is said to be completely converted into heat when:
(A) Bodies are at rest
(B) Bodies move with uniform velocity
(C) Bodies move under friction
(D) No external force acts

Ans: D
Explanation: When no external work is done (friction converts mechanical work to heat). [SSC CGL 2019]

Q2. The SI unit of work or energy is:
(A) Newton
(B) Joule
(C) Watt
(D) Pascal

Ans: B
Explanation: Work/Energy unit is Joule (J) = Newton × meter. [RRB NTPC 2021]

Q3. One horse power is equal to:
(A) 746 Watt
(B) 735 Watt
(C) 750 Watt
(D) 700 Watt

Ans: A
Explanation: 1 HP = 746 W. Common conversion question. [SSC CHSL 2020]

Q4. 1 kWh is equal to:
(A) 3.6 × 10⁴ J
(B) 3.6 × 10⁵ J
(C) 3.6 × 10⁶ J
(D) 3.6 × 10⁷ J

Ans: C
Explanation: 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J. Electricity bill unit. [RRB Group D 2018]

Q5. When is work done zero?
(A) Force ⊥ displacement
(B) Force parallel to displacement
(C) Force = 0
(D) Displacement = 0

Ans: A
Explanation: W = F × d × cos90° = 0. [SSC CGL 2022]

Q6. Work done by friction is always:
(A) Positive
(B) Zero
(C) Negative
(D) Depends on direction

Ans: C
Explanation: Friction opposes motion (θ = 180°), so cos180° = -1. [RRB ALP 2018]

Q7. Kinetic energy of a body:
(A) Is always positive
(B) Depends on mass and velocity
(C) Is same as potential energy
(D) Is measured in Newton

Ans: B
Explanation: KE = ½mv². [Delhi Police 2020]

Q8. 1 Joule is equal to:
(A) 1 Watt
(B) 1 Newton-metre
(C) 1 kg-m/s
(D) 1 Pascal

Ans: B
Explanation: 1 J = 1 N × 1 m. [SSC MTS 2017]

Q9. According to work-energy theorem:
(A) Work = Total energy
(B) Work = Change in KE
(C) Work = Power × Time
(D) Work = Force × Velocity

Ans: B
Explanation: W_net = ΔKE = KE_final - KE_initial. [UPSC CDS 2021]

Q10. If kinetic energy doubles, linear momentum becomes:
(A) Double
(B) √2 times
(C) Half
(D) 4 times

Ans: B
Explanation: KE ∝ v², P ∝ v → P ∝ √KE → √2 times. [SSC CGL 2021]

Q11. A body of mass m moving with velocity v stops after distance d. Work done by friction:
(A) Positive
(B) Zero
(C) Negative (mv²/2)
(D) mv²/2

Ans: C
Explanation: Friction does negative work = -ΔKE = -½mv². [RRB NTPC 2020]

Q12. Work done in lifting a 10 kg object by 5 m (g=10):
(A) 50 J
(B) 500 J
(C) 5000 J
(D) 50 kJ

Ans: B
Explanation: W = mgh = 10 × 10 × 5 = 500 J. [SSC CHSL 2019]

Q13. If velocity doubles, kinetic energy becomes:
(A) Double
(B) Four times
(C) Half
(D) 8 times

Ans: B
Explanation: KE ∝ v² → 2v → 4 KE. [RRB Group D 2022]

Q14. Power is the rate of:
(A) Doing work
(B) Applying force
(C) Changing energy
(D) Moving objects

Ans: A
Explanation: P = W/t. [SSC MTS 2021]

Q15. Unit of power is:
(A) Joule
(B) Newton
(C) Watt
(D) kg-m/s

Ans: C
Explanation: Watt = Joule/second. [RRB ALP 2021]

Q16. A 100 W bulb glows for 2 hours. Energy consumed:
(A) 200 J
(B) 200 Wh
(C) 0.2 kWh
(D) 720 kJ

Ans: C
Explanation: E = P × t = 100 W × 2 h = 200 Wh = 0.2 kWh. [SSC CGL 2018]

Q17. 1 horsepower = ? Watt
(A) 746
(B) 735
(C) 1000
(D) 500

Ans: A
Explanation: 1 HP = 746 W. [Delhi Police 2021]

Q18. Commercial unit of energy:
(A) Joule
(B) Watt
(C) Newton
(D) kWh

Ans: D
Explanation: kWh used in electricity bills. [RRB NTPC 2019]

Q19. According to law of conservation of energy:
(A) Energy can be created
(B) Energy can be destroyed
(C) Energy can only be transformed
(D) Total energy decreases

Ans: C
Explanation: Energy neither created nor destroyed — only changes form. [UPSC 2020]

Q20. In free fall (no friction), total mechanical energy:
(A) Increases
(B) Decreases
(C) Remains constant
(D) Becomes zero

Ans: C
Explanation: KE + PE = Constant. [SSC CHSL 2022]

Q21. Work done by gravity when object falls:
(A) Positive
(B) Negative
(C) Zero
(D) Depends on height

Ans: C
Explanation: Gravity does positive work, but conservation makes net change zero. [RRB Group D 2021]

 

Q22. A spring is compressed. Energy stored is:
(A) Kinetic energy
(B) Elastic potential energy
(C) Gravitational PE
(D) Chemical energy

Ans: B
Explanation: PE_elastic = ½kx². [SSC CGL 2020]

Q23. If mass doubles and velocity halves, kinetic energy:
(A) Doubles
(B) Halves
(C) Same
(D) 4 times

Ans: C
Explanation: KE ∝ m × v² → 2m × (½v)² = 2 × ¼ = ½ → same KE. [RRB NTPC 2021]

Q24. Satellite in circular orbit does zero work because:
(A) No motion
(B) Gravity ⊥ velocity
(C) No gravity
(D) Constant speed

Ans: B
Explanation: θ = 90°, cos90° = 0 → W = 0. [UPSC CDS 2022]

Q25. A 2 kg ball dropped from 10 m (g=10). Speed just before ground:
(A) 10 m/s
(B) 14.14 m/s
(C) 20 m/s
(D) 100 m/s

Ans: B
Explanation: mgh = ½mv² → 2×10×10 = ½×2×v² → v = √200 = 14.14 m/s. [SSC MTS 2020]

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FAQs-

Q1. What is the SI unit of work and energy?
Joule (J) = Newton-meter = kg-m²/s².

Q2. When is work done zero?
When force and displacement are perpendicular (θ = 90°, cos90° = 0).

Q3. State work-energy theorem.
Net work done on an object = Change in its kinetic energy.

Q4. What is 1 kWh in Joules?
1 kWh = 3.6 × 10⁶ Joules.

Q5. Can energy be created or destroyed?
No. Energy can only be transformed (Law of Conservation).

Q6. Difference between work and power?
Work = Energy (Joule), Power = Work/Time (Watt).

Q7. Formula for kinetic energy?
KE = ½mv².

Q8. When does friction do negative work?
When it opposes motion (always negative work).

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Conclusion

Work, Energy and Power is not a difficult chapter — it just requires clear concepts of 9 basic formulas, understanding of conservation principle, and practice of 10–15 numerical problems. For UPSC, SSC, RRB and other competitive exams, you don't need JEE-level complexity — just remember:

Key Exam Formulas (Memorise These):

Work: W = F × d × cosθ

Kinetic Energy: KE = ½mv² 

Potential Energy: PE = mgh

Power: P = W/t = F × v

Work-Energy Theorem: W_net = ΔKE

Conservation: KE₁ + PE₁ = KE₂ + PE₂

1 kWh = 3.6 × 10⁶ J