Work, Energy and Power: Formulas, Examples, Tricks and MCQs

In everyday language, we say we are "working" when we study or think hard. In physics, however, work has a very exact meaning – it is done only when a force moves an object. The ability to do work is called energy, and the rate at which work is done is called power. These three ideas connect everything from a coolie lifting luggage and a waterfall turning turbines to the electricity bill in our homes.

Work, energy and power is a high-scoring Physics topic in SSC CGL, CHSL, MTS, GD, RRB NTPC, Group D, ALP, JE, WBCS, Police and State PSC exams. Questions are asked on the conditions for work, positive, negative and zero work, kinetic and potential energy, the work–energy theorem, conservation of energy, energy conversions, units like joule, watt, horsepower and kilowatt-hour, and collisions. This guide explains everything in simple language with diagrams, formulas, solved examples, memory tricks and 20 MCQs with answers.

➤ Work: W = F s cos θ · SI unit joule (J) · Scalar quantity
➤ Zero work: When force is perpendicular to displacement (θ = 90°) or there is no displacement
➤ Kinetic energy: KE = ½mv² · Doubling velocity makes KE four times
➤ Potential energy: PE = mgh (gravitational) · ½kx² (spring)
➤ Work–energy theorem: Work done by net force = change in kinetic energy
➤ Power: P = W/t = Fv · SI unit watt (W) · 1 horsepower = 746 W
➤ Commercial unit of energy: 1 kWh = 1 "unit" = 3.6 × 10⁶ J

What is Work?

Work is said to be done when a force acting on an object moves it through some distance in the direction of the force. Two conditions must both be satisfied: (1) a force must act, and (2) the object must be displaced. If either is missing, no work is done in the physics sense – a person pushing hard against a wall that does not move does no work, however tired he feels.

W = F × s × cos θ

where F is the force, s is the displacement and θ is the angle between the force and the displacement (Figure 1). Work is a scalar quantity. Its SI unit is the joule (J): 1 joule is the work done when a force of 1 newton moves an object by 1 metre in its own direction. The CGS unit is the erg (1 J = 10⁷ erg).

Figure 1: When a force acts at an angle θ, only its component along the displacement (F cos θ) does work

Positive, Negative and Zero Work

Example 1: A force of 10 N moves a box 5 m. (a) If the force is along the displacement: W = 10 × 5 × cos 0° = 50 J. (b) If the force acts at 60°: W = 10 × 5 × cos 60° = 10 × 5 × 0.5 = 25 J.

Energy – The Capacity to Do Work

The energy of a body is its capacity to do work. A body that does work loses energy, and a body on which work is done gains energy. Energy is a scalar and has the same unit as work – the joule.

Units of Energy

Kinetic Energy

The energy a body has because of its motion is called kinetic energy (KE). A moving hammer drives a nail, flowing water turns a turbine, and wind turns a windmill – all because of kinetic energy.

KE = ½ m v²

• KE depends on the square of velocity: if velocity is doubled, KE becomes 4 times; if tripled, 9 times. This is why accidents at high speed are so dangerous.
• KE is always positive (or zero) – it can never be negative.
• Relation with momentum: KE = p² / 2m and p = √(2m × KE). If two bodies have the same KE, the heavier one has more momentum.

Example 2: A 2 kg ball moves at 10 m/s. KE = ½ × 2 × 10² = 100 J. If its speed becomes 20 m/s, KE = ½ × 2 × 400 = 400 J – four times.

Potential Energy

The energy a body has because of its position or configuration (shape) is called potential energy (PE). Water stored in a dam, a book on a high shelf, a stretched rubber band, a compressed spring and a wound-up watch spring all have potential energy.

Example 3: A 5 kg box is lifted to a shelf 10 m high (g = 10 m/s²). PE = mgh = 5 × 10 × 10 = 500 J. The work done in lifting it is also 500 J, whatever path is taken – because gravity is a conservative force, the work done against it depends only on the initial and final heights.

Work–Energy Theorem

Statement: The work done by the net force on a body is equal to the change in its kinetic energy.

W = ½ m v² − ½ m u² = KE_final − KE_initial

If positive work is done on a body, its KE increases (it speeds up). If negative work is done – for example by friction or brakes – its KE decreases (it slows down).

Example 4: A 1,000 kg car moving at 20 m/s is brought to rest. Work done by the brakes = 0 − ½ × 1,000 × 20² = −2,00,000 J (2 × 10⁵ J of kinetic energy is converted into heat in the brakes).

Law of Conservation of Energy

Statement: Energy can neither be created nor destroyed; it can only be changed from one form to another. The total energy of an isolated system remains constant.

In mechanical systems where only gravity acts (no friction), the total mechanical energy (KE + PE) stays constant. A freely falling body is the classic example (Figure 2). At the top, all energy is potential; as it falls, PE turns into KE; just before hitting the ground, all energy is kinetic. A swinging pendulum continuously exchanges PE and KE in the same way – maximum PE at the extreme positions and maximum KE at the lowest (mean) position.

Figure 2: Conservation of energy in free fall – potential energy (blue) changes into kinetic energy (red), but the total stays the same

Example 5: A 2 kg ball is dropped from 20 m (g = 10 m/s²). PE at the top = 2 × 10 × 20 = 400 J. Just before hitting the ground, KE = 400 J, so ½ × 2 × v² = 400, v² = 400, v = 20 m/s – the same answer as v = √(2gh).

Energy Conversion Devices

Mass–energy equivalence: Albert Einstein showed in 1905 that mass itself is a form of energy: E = mc², where c is the speed of light (3 × 10⁸ m/s). A tiny loss of mass releases a huge amount of energy – the basis of nuclear power and of the Sun's energy.

Power – How Fast Work is Done

Power is the rate of doing work or the rate at which energy is transferred. Two people may climb the same staircase and do the same work, but the one who climbs faster has more power.

P = W / t and also P = F × v

Important: The kilowatt-hour (kWh) is a unit of energy, not power. It is the energy used by a 1 kW appliance in 1 hour. One kWh is one "unit" on an electricity bill.

Example 6: A 60 kg student climbs a 10 m high staircase in 20 s (g = 10 m/s²). Work = mgh = 60 × 10 × 10 = 6,000 J. Power = 6,000 ÷ 20 = 300 W (about 0.4 hp).

Example 7 (electricity bill): A 100 W bulb is used for 10 hours a day for 30 days. Energy = 0.1 kW × 10 h × 30 = 30 kWh (30 units). At ₹6 per unit, the cost is ₹180.

Efficiency

No machine converts all input energy into useful work – some is always lost as heat, sound or friction. Efficiency = (Useful output energy ÷ Input energy) × 100%. Efficiency is always less than 100% in real machines. LED bulbs are far more efficient than ordinary filament bulbs because they waste much less energy as heat.

Collisions

When two bodies hit each other, momentum is always conserved (if no external force acts), but kinetic energy may or may not be conserved (Figure 3).

Figure 3: In an elastic collision both momentum and kinetic energy are conserved; in an inelastic collision only momentum is conserved

Special result: When two bodies of equal mass collide elastically head-on, they exchange their velocities – a moving ball stops and the ball at rest moves off with the same speed (as in Newton's cradle and in carrom).

Example 8: A 2 kg ball moving at 3 m/s hits a 1 kg ball at rest and they stick together. By conservation of momentum: 2 × 3 = (2 + 1) × v, so v = 2 m/s. KE before = ½ × 2 × 9 = 9 J; KE after = ½ × 3 × 4 = 6 J. So 3 J is lost as heat and sound.

Work, Energy and Power – Formula Sheet

West Bengal Connection – Energy from Height and Heat

West Bengal shows energy conversion on a large scale. The Sidrapong hydroelectric power station near Darjeeling, commissioned in 1897, was India's first hydropower station – it converted the potential energy of falling water into electricity. The Purulia Pumped Storage Project (900 MW) in the Ayodhya Hills of Purulia district works like a giant battery: when electricity demand is low, water is pumped up to an upper reservoir (storing potential energy, mgh); when demand is high, it is released to run turbines and generate electricity. The Damodar Valley Corporation (set up in 1948) runs hydel stations at Maithon and Panchet, while large thermal power stations such as NTPC's Farakka plant convert the chemical energy of coal into heat and then electricity. Kolkata's CESC, supplying the city since the late 1890s, was one of India's earliest electricity utilities.

For related science, read Light Reflection and Refraction and Carbon and Organic Chemistry (the chemistry of fuels). Energy and the economy are linked – see Economic Planning: From Five-Year Plans to NITI Aayog – and solar energy drives the winds explained in Climatology. Practise with the CSIR NAL MTS Mock Test.

20 MCQs on Work, Energy and Power

Q1. The SI unit of work is:
(a) Watt
(b) Joule
(c) Newton
(d) Pascal

Answer: (b) – 1 joule = 1 newton × 1 metre; watt is the unit of power.

Q2. Work done is zero when the angle between force and displacement is:
(a) 90°
(b) 0°
(c) 45°
(d) 180°

Answer: (a) – W = Fs cos 90° = 0.

Q3. A coolie carrying a load on his head walks on a level platform. The work done by him against gravity is:
(a) Positive
(b) Negative
(c) Zero
(d) Maximum

Answer: (c) – The force he applies is vertical, while displacement is horizontal.

Q4. The work done by friction on a moving body is generally:
(a) Positive
(b) Zero
(c) Infinite
(d) Negative

Answer: (d) – Friction acts opposite to the direction of motion.

Q5. A force of 20 N moves a body 4 m along its direction. The work done is:
(a) 5 J
(b) 24 J
(c) 80 J
(d) 16 J

Answer: (c) – W = F × s = 20 × 4 = 80 J.

Q6. The work done by the gravitational force on a satellite moving in a circular orbit is:
(a) Zero
(b) Positive
(c) Negative
(d) Equal to its kinetic energy

Answer: (a) – Gravity acts towards the centre, perpendicular to the satellite's motion.

Q7. If the velocity of a body is doubled, its kinetic energy becomes:
(a) Double
(b) Half
(c) Unchanged
(d) Four times

Answer: (d) – KE = ½mv², so KE ∝ v²; (2)² = 4.

Q8. The kinetic energy of a 4 kg body moving at 5 m/s is:
(a) 20 J
(b) 50 J
(c) 100 J
(d) 10 J

Answer: (b) – KE = ½ × 4 × 25 = 50 J.

Q9. Water stored in a dam possesses:
(a) Kinetic energy
(b) Potential energy
(c) Electrical energy
(d) Chemical energy

Answer: (b) – It has gravitational PE due to its height; when released, it turns into KE and then electrical energy.

Q10. A 10 kg body is raised to a height of 5 m. Its potential energy is (g = 10 m/s²):
(a) 50 J
(b) 15 J
(c) 500 J
(d) 2 J

Answer: (c) – PE = mgh = 10 × 10 × 5 = 500 J.

Q11. According to the work–energy theorem, the work done by the net force on a body equals the change in its:
(a) Potential energy
(b) Momentum
(c) Power
(d) Kinetic energy

Answer: (d) – W = ½mv² − ½mu².

Q12. In a simple pendulum, kinetic energy is maximum at the:
(a) Mean (lowest) position
(b) Extreme positions
(c) Midway between mean and extreme
(d) KE is the same everywhere

Answer: (a) – At the lowest point PE is minimum and KE is maximum; at the extremes KE is zero.

Q13. Which statement expresses the law of conservation of energy?
(a) Energy can be created but not destroyed
(b) Energy can neither be created nor destroyed, only transformed
(c) Energy is always lost in a machine
(d) Energy can be destroyed but not created

Answer: (b) – The total energy of an isolated system remains constant.

Q14. An electric motor converts:
(a) Mechanical energy into electrical energy
(b) Chemical energy into electrical energy
(c) Electrical energy into mechanical energy
(d) Heat energy into electrical energy

Answer: (c) – A generator does the reverse (mechanical → electrical).

Q15. The SI unit of power is:
(a) Joule
(b) Kilowatt-hour
(c) Horsepower
(d) Watt

Answer: (d) – 1 W = 1 J/s; horsepower is a non-SI unit and kWh is a unit of energy.

Q16. One horsepower is equal to:
(a) 746 W
(b) 1,000 W
(c) 100 W
(d) 3.6 × 10⁶ W

Answer: (a) – 1 hp ≈ 746 W, a unit introduced by James Watt.

Q17. One kilowatt-hour (kWh) is equal to:
(a) 1,000 J
(b) 3.6 × 10³ J
(c) 3.6 × 10⁶ J
(d) 746 J

Answer: (c) – 1 kWh = 1,000 W × 3,600 s = 3.6 × 10⁶ J; it is the "unit" on electricity bills.

Q18. A person of mass 50 kg climbs 12 m in 30 s. His power is (g = 10 m/s²):
(a) 20 W
(b) 200 W
(c) 600 W
(d) 6,000 W

Answer: (b) – Work = mgh = 50 × 10 × 12 = 6,000 J; power = 6,000 ÷ 30 = 200 W.

Q19. In an inelastic collision, which quantity is conserved?
(a) Kinetic energy only
(b) Both momentum and kinetic energy
(c) Neither momentum nor kinetic energy
(d) Momentum only

Answer: (d) – Momentum is conserved in all collisions; kinetic energy is conserved only in elastic collisions.

Q20. India's first hydroelectric power station, commissioned in 1897, is located at:
(a) Sidrapong, Darjeeling
(b) Shivanasamudra, Karnataka
(c) Bhakra, Himachal Pradesh
(d) Maithon, Jharkhand

Answer: (a) – The Sidrapong station in Darjeeling, West Bengal, began in 1897; Shivanasamudra (1902) on the Kaveri was among the first major hydel plants in Asia.

Want more practice? Try our Daily GK Quiz and Mock Tests.

Conclusion

Work, energy and power are closely linked ideas. Work is done only when a force causes displacement; energy is the capacity to do that work and exists as kinetic and potential energy among many other forms; and power tells us how fast the work is done. The law of conservation of energy and the work–energy theorem solve a wide range of problems, while collisions show the difference between conservation of momentum and conservation of kinetic energy. For exams, remember W = Fs cos θ, KE = ½mv², PE = mgh, P = W/t, the meaning of zero and negative work, units like joule, watt, horsepower and kWh, and the main energy conversions. Revise the tricks above and practise the numericals regularly.

Reference: NCERT Science Class IX ("Work and Energy"); NCERT Physics Class XI ("Work, Energy and Power").