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Work, Energy and Power – Class 11 Physics notes, important questions and MCQs

NCERT Class 11 Physics, chapter 5. Notes, key terms, important questions with answers and MCQs.

Chapter overview

Work is done when a force moves a body. Energy is the capacity to do work; the work–energy theorem and conservation of energy solve many problems, and power is the rate of doing work.

Work and energy

W = F·s = Fs cos θ; work by a variable force = ∫F dx.
Kinetic energy K = ½mv² = p²/2m; work–energy theorem W_net = ΔK.
Potential energy: gravitational mgh; spring ½kx²; mechanical energy is conserved for conservative forces.

Power and collisions

Power P = W/t = F·v; 1 hp = 746 W; 1 kWh = 3.6 × 10⁶ J.
Elastic collision conserves momentum and KE; inelastic conserves only momentum.
1-D elastic collision with equal masses: velocities are exchanged.

Key terms

Conservative force: force whose work does not depend on path (gravity, spring)
Power: rate of doing work
Coefficient of restitution: e = relative speed of separation / relative speed of approach; e = 1 elastic, e = 0 perfectly inelastic

Formulas

W = Fs cos θ
K = p²/2m
P = Fv

Important questions with answers

Show that the work done by gravity in moving a body along a closed path is zero.2 marks

Gravity is conservative: work depends only on initial and final heights, W = mg(h₁ − h₂). For a closed path h₁ = h₂, so W = 0.

State and prove the work–energy theorem for a constant force.3 marks

The net work done on a body equals the change in its kinetic energy. For constant force F: v² = u² + 2as, so ½mv² − ½mu² = mas = Fs = W.

A 2 kg ball is dropped from 5 m on a hard floor and rebounds to 3.2 m (g = 10 m/s²). Find the speeds just before and after impact, the coefficient of restitution and the energy lost.5 marks

Before: v₁ = √(2gh₁) = √100 = 10 m/s. After: v₂ = √(2 × 10 × 3.2) = √64 = 8 m/s. e = v₂/v₁ = 0.8. Energy lost = mg(h₁ − h₂) = 2 × 10 × 1.8 = 36 J (as heat and sound).

Quick revision

Work–energy theorem: W = ΔK.
Friction is non-conservative.
Elastic: KE conserved.

Exam tips

If momentum is the same, the lighter body has more KE.
Work done by friction is negative and converts mechanical energy into heat; use W_nc = ΔE for such problems.

Practice MCQs

SI unit of power is
1. joule
2. pascal
3. newton
4. watt
Show answer
Answer: (d) watt. J/s.
Work done when force is perpendicular to displacement is
1. maximum
2. negative
3. zero
4. infinite
Show answer
Answer: (c) zero. cos 90° = 0.
KE of a 2 kg body moving at 3 m/s is
1. 6 J
2. 3 J
3. 18 J
4. 9 J
Show answer
Answer: (d) 9 J. ½ × 2 × 9.
If the speed of a body doubles, its KE becomes
1. double
2. four times
3. half
4. same
Show answer
Answer: (b) four times. KE ∝ v².
A pump lifts 100 kg of water to a height of 10 m in 20 s (g = 10). Its power is
1. 50 W
2. 200 W
3. 5000 W
4. 500 W
Show answer
Answer: (d) 500 W. mgh/t = 10,000/20.
A spring (k = 200 N/m) is compressed by 0.1 m. Energy stored is
1. 1 J
2. 2 J
3. 10 J
4. 20 J
Show answer
Answer: (a) 1 J. ½ × 200 × 0.01.
In an elastic collision between equal masses with one at rest, after collision
1. both move together
2. velocities are exchanged
3. both stop
4. the moving one bounces back with the same speed
Show answer
Answer: (b) velocities are exchanged. Exchange of velocities.
A body of mass 2 kg moving at 4 m/s collides with an identical body at rest and they stick together. Loss of KE is
1. 0 J
2. 16 J
3. 8 J
4. 4 J
Show answer
Answer: (c) 8 J. 16 J − 8 J.

All chapters of Class 11 Physics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.