Is it correct to say: Assuming work is done whenever a force is applied?

If displacement is zero (holding a suitcase still) or force perpendicular to motion (coolie walking with load on head), W = 0.

Is it correct to say: Using formula PE = mgh far from Earth's surface?

PE = mgh applies only when g is nearly constant (small heights). For satellites, use PE = −GMm/r.

Is it correct to say: Confusing power and energy units?

Energy → J or kWh. Power → W or kW. 1 kWh is energy, 1 kW is power.

Is it correct to say: Taking KE as negative for a body moving backward?

KE = ½mv² is always positive because v² ≥ 0. Direction is not encoded.

Is it correct to say: Forgetting cosθ when force is at an angle?

For a pulled sledge, use W = Fs cosθ, where θ is the pulling angle.

Is it correct to say: Adding PE and KE with different reference heights?

Choose one reference level (usually ground) for all PE calculations in a problem.

Work, Energy and Power

Work, kinetic energy, potential energy, work–energy theorem, power — Maharashtra Board Class 10 Physics

📐 8 formulas✏️ 3 examples🎯 5 practice⚖️ 4 marks🏫 Maharashtra State Board📚 Class 10✓ 2025–26 syllabus

💡

Board Exam Tips

→Definition of 1 joule (work) and 1 watt (power) are 1-mark repeat asks.
→Derive KE = ½mv² using v² = u² + 2as — a favourite 3-mark question.
→Work–energy theorem numericals appear regularly — practise both algebraic and graphical form.
→1 kWh = 3.6×10⁶ J — commercial vs SI unit conversion is asked.
→Only the component of force along displacement does work — remember the cosθ factor.

📊 Diagram

Force at angle θ with displacement — component F cosθ does work

📐 Formulas(8)

Work Done by a Constant Force★ Board fav

W = F s cos θ

Symbol	Meaning
$W$	Work done (J)
$F$	Applied force (N)
$s$	Displacement (m)
$θ$	Angle between force and displacement

Kinetic Energy★ Board fav

K E = \frac{1}{2} m v^{2}

Gravitational Potential Energy

P E = m g h

Work–Energy Theorem★ Board fav

W_{n e t} = Δ K E = \frac{1}{2} m v^{2} - \frac{1}{2} m u^{2}

Power (Average)

P = \frac{W}{t}

Power (Instantaneous)

P = F v

Conservation of Mechanical Energy

K E + P E = constant

Commercial Unit of Energy

1 kWh = 3.6 \times 1 0^{6} J

✏️ Solved Examples

1Solved Exampleeasy3 steps

A body of mass 5 kg is lifted vertically upward through a height of 2 m. Find the work done. (g = 10 m/s²)

Force required to lift = weight of body

F = m g = 5 \times 10 = 50 N

2Solved Exampleboard4 steps

An engine pumps 100 kg of water to a height of 20 m in 10 s. Find its power. (g = 10 m/s²)

Work done against gravity

W = m g h = 100 \times 10 \times 20

3Solved ExampleHOTS4 steps

A ball of mass 0.2 kg is dropped from a height of 5 m. Find (i) PE at top, (ii) KE just before hitting ground, (iii) velocity of impact. Use g = 10 m/s². Neglect air resistance.

PE at top (reference: ground)

P E = m g h = 0.2 \times 10 \times 5 = 10 J

⚠️ Traps & Common Mistakes

⚠️Common Mistakes6

1
Assuming work is done whenever a force is applied
✓If displacement is zero (holding a suitcase still) or force perpendicular to motion (coolie walking with load on head), W = 0.
2
Using formula PE = mgh far from Earth's surface
✓PE = mgh applies only when g is nearly constant (small heights). For satellites, use PE = −GMm/r.
3
Confusing power and energy units
✓Energy → J or kWh. Power → W or kW. 1 kWh is energy, 1 kW is power.
4
Taking KE as negative for a body moving backward
✓KE = ½mv² is always positive because v² ≥ 0. Direction is not encoded.
5
Forgetting cosθ when force is at an angle
✓For a pulled sledge, use W = Fs cosθ, where θ is the pulling angle.
6
Adding PE and KE with different reference heights
✓Choose one reference level (usually ground) for all PE calculations in a problem.

🎯 Practice Yourself

🎯Practice Yourself5 questions

Q1
Calculate the KE of a car of mass 1000 kg moving with a velocity of 20 m/s.
Q2
An electric bulb of 60 W is used for 5 hours daily. Calculate the energy consumed in 30 days in kWh.
Q3
How much work is done in pushing a wall for 5 minutes if the wall does not move?
Q4
A body of mass 2 kg falls from a height of 10 m. Find its velocity just before touching the ground. (g = 10 m/s²)
Q5
Define 1 joule of work.

📝 Notes

Work, Energy and Power — Maharashtra SSC

Maharashtra Board treats Work, Energy and Power as a compact chapter with clear formulas but tricky conceptual questions.

What counts as work?

Three conditions must hold simultaneously:

A force must act on the body.
The body must be displaced.
Force and displacement must have a component along the same line.

Positive, negative and zero work

Positive: force and displacement in the same direction (θ < 90°). Example: lifting a load.
Negative: force opposes displacement (θ > 90°). Example: friction.
Zero: perpendicular (θ = 90°) or no displacement. Example: coolie carrying weight horizontally.

Energy — many forms, one currency

Kinetic, potential, thermal, chemical, electrical, nuclear — all interconvertible. In mechanics, KE and PE dominate. In a lossless system, their sum is constant (conservation).

Power — how fast, not how much

Two engines can do the same work; the one that does it in less time is more powerful. That is why we quote engine ratings in kW or hp.

Board vs CBSE

CBSE covers this in Class 9 with similar depth. Maharashtra SSC's Class 10 treatment adds commercial unit conversion (kWh ↔ J) and slightly more numerical variety around lifts and pumps.