work energy power formulas pyqs

Work Energy Power Formulas PYQs

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Class 11 Physics - Work Energy Power

Work Energy Power Formula Sheet and PYQs

Complete revision page with formulas, NCERT questions, CBSE PYQs, NEET PYQs, JEE PYQs and quick revision notes.

NCERTCBSENEETJEE MainJEE AdvancedIBIGCSEA-Level
01

Complete Formula Sheet

All high-frequency Work, Energy and Power formulas in clean revision tables.

TopicFormulaUse
WorkW = F.s = Fs cos thetaConstant force and displacement
Variable forceW = ∫F dxArea under F-x graph
Spring workW = 1/2 kx2Work needed to stretch or compress spring
Kinetic energyK = 1/2 mv2Energy due to motion
Work-energy theoremWnet = ΔKFastest route for speed-change problems
Potential energyU = mghNear Earth surface
Elastic PEU = 1/2 kx2Spring storage
Mechanical energyK + U = constantOnly conservative forces
PowerP = W/t = dW/dt = F.vRate of energy transfer
Efficiencyη = useful output/inputUse energy or power ratio
Horsepower1 HP = 746 WEngines and motors
Collisionsmomentum conserved, e = separation/approach, loss = 1/2 mu(1-e2)u2Direct collisions
02

Work Formulae

Positive, negative, zero, constant-force, variable-force, graph and spring work.

Sign of Work

W = Fs cos theta

Positive if theta < 90 degrees, negative if theta > 90 degrees, zero if theta = 90 degrees.

Variable Force

W = ∫x1x2 F(x) dx

For changing force, use integration or graph area.

Spring

Wexternal = 1/2 kx2

Work by spring during stretch is negative: -1/2kx2.

xFArea = Work
03

Energy Formulae

Kinetic, potential, spring, conservative and non-conservative energy relations.

Kinetic Energy

K = 1/2 mv2

Doubling speed makes KE four times.

Potential Energy

U = mgh

Depends on chosen zero level.

Non-conservative Work

Wnc = Δ(K+U)

Friction reduces mechanical energy.

Collisions

KE loss = heat + sound + deformation

Momentum may remain conserved while KE changes.

Conservation

K1 + U1 = K2 + U2

Use when no friction or external loss.

Friction Loss

Wf = -f s

For kinetic friction on a path of length s.

04

Power Formulae

Average, instantaneous, lifting, vehicles, machines, horsepower and efficiency.

CaseFormulaMini Example
Average powerP = W/t500 J in 10 s gives 50 W
Instantaneous powerP = dW/dtIf W=t2, P=2t
Force and velocityP = Fv cos theta100 N at 5 m/s gives 500 W
LiftingP = mgh/tUseful for cranes and lifts
VehiclesP = resistive force x speedAt constant speed
Machinesη = Pout/Pin80% means 0.8 useful fraction

Searching for a Physics Tutor? If Work, Energy, Power, F-x graphs, spring energy or tough numericals are not clear, contact Kumar Sir.

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05

NCERT Examples

Question, given, formula, calculation, final answer and exam tip.

Example 1: Work by inclined force
Question: A 20 N force acts at 60 degrees and moves a box 5 m.
Given: F=20 N, s=5 m, theta=60 degrees
Formula: W=Fs cos theta
Calculation: W=20 x 5 x 0.5 = 50 J
Final Answer: 50 J
Exam Tip: Resolve force along displacement first.
Example 2: Work-energy theorem
Question: A 2 kg object speeds up from 2 m/s to 6 m/s.
Given: m=2 kg, u=2 m/s, v=6 m/s
Formula: Wnet=1/2m(v2-u2)
Calculation: W=1 x (36-4)=32 J
Final Answer: 32 J
Exam Tip: Net work, not individual work, equals Delta K.
Example 3: Spring energy
Question: A 400 N/m spring is compressed 0.20 m.
Given: k=400 N/m, x=0.20 m
Formula: U=1/2kx2
Calculation: U=0.5 x 400 x 0.04 = 8 J
Final Answer: 8 J
Exam Tip: Spring energy is never kx only.
Example 4: Power in lifting
Question: A 50 kg load is lifted 4 m in 10 s.
Given: m=50 kg, h=4 m, t=10 s
Formula: P=mgh/t
Calculation: P=50 x 9.8 x 4 / 10 = 196 W
Final Answer: 196 W
Exam Tip: Use time only in power, not in work.
Example 5: Efficiency
Question: A motor takes 1000 W and gives 750 W useful output.
Given: Pin=1000 W, Pout=750 W
Formula: eta=Pout/Pin
Calculation: eta=0.75
Final Answer: 75%
Exam Tip: Efficiency has no unit.
06

NCERT Exercises

Solved exercise-style questions covering work, energy, power, spring, conservation, collisions and graphs.

1. Work: A porter carries a bag horizontally at constant height. Work by gravity?
Zero, because gravity is vertical and displacement is horizontal.
2. Energy: A 1 kg stone dropped from 20 m. Speed before ground neglecting air?
v=sqrt(2gh)=sqrt(392)=19.8 m/s.
3. Power: A pump raises 200 kg water by 5 m every second. Power?
P=mgh/t=200x9.8x5=9800 W.
4. Spring: Find work needed to stretch k=100 N/m spring by 0.3 m.
W=1/2kx2=4.5 J.
5. Conservation: A body starts from rest at height 10 m. KE at height 4 m?
K=mg(10-4)=6mg.
6. Collisions: Why is KE not conserved when bodies stick?
Internal deformation, heat and sound take part of KE.
7. Graphs: A rectangle F-x graph has F=8 N from 0 to 5 m. Work?
Area=40 J.
07

CBSE PYQs

Board-style short answers, long answers, numericals and case-based practice.

1. CBSE board-style question: Short answer: Define one joule.
One joule is work done when 1 N force displaces a body by 1 m in force direction.
2. CBSE board-style question: Short answer: State work-energy theorem.
Net work done on a body equals change in kinetic energy.
3. CBSE board-style question: Long answer: Explain conservation of mechanical energy for a freely falling body.
At height h, energy is mgh. During fall, GPE decreases and KE increases. Neglecting air resistance, K+U remains constant.
4. CBSE board-style question: Numerical: A 10 kg body is lifted by 2 m. Find work against gravity.
W=mgh=10x9.8x2=196 J.
5. CBSE board-style question: Numerical: A 100 W bulb runs for 10 s. Energy used?
E=Pt=1000 J.
6. CBSE board-style question: Case-based: Brakes stop a bicycle.
Brakes do negative work; kinetic energy becomes thermal energy. Larger speed means much larger stopping distance.
7. CBSE board-style question: Numerical: A 4 kg body at 5 m/s. KE?
K=50 J.
8. CBSE board-style question: Long answer: Distinguish conservative and non-conservative forces.
Conservative work is path independent; non-conservative work depends on path and changes mechanical energy.
08

NEET PYQs

50 NEET-style MCQs. Authentic year is not invented; these are marked exam-style.

1. NEET Exam-style Question: A force of 10 N acts at 60 degrees to displacement 4 m. Work done is closest to: A 10 J B 20 J C 40 J D 80 J
Correct Answer: B. W = Fs cos theta = 10 x 4 x 1/2 = 20 J.
Detailed Explanation: This question tests work by constant force. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
2. NEET Exam-style Question: A 2 kg body moves with speed 5 m/s. Its kinetic energy is: A 10 J B 25 J C 50 J D 100 J
Correct Answer: B. K = 1/2 mv2 = 25 J.
Detailed Explanation: This question tests kinetic energy. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
3. NEET Exam-style Question: A machine does 600 J work in 20 s. Average power is: A 20 W B 30 W C 60 W D 120 W
Correct Answer: B. P = W/t = 30 W.
Detailed Explanation: This question tests power. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
4. NEET Exam-style Question: A spring k = 200 N/m is compressed by 0.10 m. Stored energy is: A 0.5 J B 1 J C 2 J D 10 J
Correct Answer: B. U = 1/2 kx2 = 1 J.
Detailed Explanation: This question tests spring energy. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
5. NEET Exam-style Question: A body falls freely from height h. Just before ground, speed is: A gh B sqrt(gh) C sqrt(2gh) D 2gh
Correct Answer: C. mgh = 1/2 mv2.
Detailed Explanation: This question tests conservation of energy. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
6. NEET Exam-style Question: Work done by friction is usually: A positive B negative C zero always D infinite
Correct Answer: B. Friction usually opposes displacement.
Detailed Explanation: This question tests frictional loss. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
7. NEET Exam-style Question: Area under force-displacement graph gives: A power B work C pressure D momentum
Correct Answer: B. Work = integral F dx.
Detailed Explanation: This question tests F-x graph. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
8. NEET Exam-style Question: A machine input is 500 J and useful output is 350 J. Efficiency is: A 35% B 50% C 70% D 100%
Correct Answer: C. eta = output/input = 0.70.
Detailed Explanation: This question tests efficiency. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
9. NEET Exam-style Question: Net work done on a body equals change in: A momentum B kinetic energy C force D power
Correct Answer: B. Wnet = Delta K.
Detailed Explanation: This question tests work-energy theorem. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
10. NEET Exam-style Question: In an inelastic collision, which is always conserved for an isolated system? A KE B momentum C speed D power
Correct Answer: B. Momentum is conserved; KE may be lost.
Detailed Explanation: This question tests collision energy. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
11. NEET Exam-style Question: A force of 10 N acts at 60 degrees to displacement 4 m. Work done is closest to: A 10 J B 20 J C 40 J D 80 J
Correct Answer: B. W = Fs cos theta = 10 x 4 x 1/2 = 20 J.
Detailed Explanation: This question tests work by constant force. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
12. NEET Exam-style Question: A 2 kg body moves with speed 5 m/s. Its kinetic energy is: A 10 J B 25 J C 50 J D 100 J
Correct Answer: B. K = 1/2 mv2 = 25 J.
Detailed Explanation: This question tests kinetic energy. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
13. NEET Exam-style Question: A machine does 600 J work in 20 s. Average power is: A 20 W B 30 W C 60 W D 120 W
Correct Answer: B. P = W/t = 30 W.
Detailed Explanation: This question tests power. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
14. NEET Exam-style Question: A spring k = 200 N/m is compressed by 0.10 m. Stored energy is: A 0.5 J B 1 J C 2 J D 10 J
Correct Answer: B. U = 1/2 kx2 = 1 J.
Detailed Explanation: This question tests spring energy. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
15. NEET Exam-style Question: A body falls freely from height h. Just before ground, speed is: A gh B sqrt(gh) C sqrt(2gh) D 2gh
Correct Answer: C. mgh = 1/2 mv2.
Detailed Explanation: This question tests conservation of energy. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
16. NEET Exam-style Question: Work done by friction is usually: A positive B negative C zero always D infinite
Correct Answer: B. Friction usually opposes displacement.
Detailed Explanation: This question tests frictional loss. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
17. NEET Exam-style Question: Area under force-displacement graph gives: A power B work C pressure D momentum
Correct Answer: B. Work = integral F dx.
Detailed Explanation: This question tests F-x graph. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
18. NEET Exam-style Question: A machine input is 500 J and useful output is 350 J. Efficiency is: A 35% B 50% C 70% D 100%
Correct Answer: C. eta = output/input = 0.70.
Detailed Explanation: This question tests efficiency. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
19. NEET Exam-style Question: Net work done on a body equals change in: A momentum B kinetic energy C force D power
Correct Answer: B. Wnet = Delta K.
Detailed Explanation: This question tests work-energy theorem. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
20. NEET Exam-style Question: In an inelastic collision, which is always conserved for an isolated system? A KE B momentum C speed D power
Correct Answer: B. Momentum is conserved; KE may be lost.
Detailed Explanation: This question tests collision energy. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
21. NEET Exam-style Question: A force of 10 N acts at 60 degrees to displacement 4 m. Work done is closest to: A 10 J B 20 J C 40 J D 80 J
Correct Answer: B. W = Fs cos theta = 10 x 4 x 1/2 = 20 J.
Detailed Explanation: This question tests work by constant force. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
22. NEET Exam-style Question: A 2 kg body moves with speed 5 m/s. Its kinetic energy is: A 10 J B 25 J C 50 J D 100 J
Correct Answer: B. K = 1/2 mv2 = 25 J.
Detailed Explanation: This question tests kinetic energy. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
23. NEET Exam-style Question: A machine does 600 J work in 20 s. Average power is: A 20 W B 30 W C 60 W D 120 W
Correct Answer: B. P = W/t = 30 W.
Detailed Explanation: This question tests power. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
24. NEET Exam-style Question: A spring k = 200 N/m is compressed by 0.10 m. Stored energy is: A 0.5 J B 1 J C 2 J D 10 J
Correct Answer: B. U = 1/2 kx2 = 1 J.
Detailed Explanation: This question tests spring energy. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
25. NEET Exam-style Question: A body falls freely from height h. Just before ground, speed is: A gh B sqrt(gh) C sqrt(2gh) D 2gh
Correct Answer: C. mgh = 1/2 mv2.
Detailed Explanation: This question tests conservation of energy. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
26. NEET Exam-style Question: Work done by friction is usually: A positive B negative C zero always D infinite
Correct Answer: B. Friction usually opposes displacement.
Detailed Explanation: This question tests frictional loss. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
27. NEET Exam-style Question: Area under force-displacement graph gives: A power B work C pressure D momentum
Correct Answer: B. Work = integral F dx.
Detailed Explanation: This question tests F-x graph. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
28. NEET Exam-style Question: A machine input is 500 J and useful output is 350 J. Efficiency is: A 35% B 50% C 70% D 100%
Correct Answer: C. eta = output/input = 0.70.
Detailed Explanation: This question tests efficiency. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
29. NEET Exam-style Question: Net work done on a body equals change in: A momentum B kinetic energy C force D power
Correct Answer: B. Wnet = Delta K.
Detailed Explanation: This question tests work-energy theorem. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
30. NEET Exam-style Question: In an inelastic collision, which is always conserved for an isolated system? A KE B momentum C speed D power
Correct Answer: B. Momentum is conserved; KE may be lost.
Detailed Explanation: This question tests collision energy. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
31. NEET Exam-style Question: A force of 10 N acts at 60 degrees to displacement 4 m. Work done is closest to: A 10 J B 20 J C 40 J D 80 J
Correct Answer: B. W = Fs cos theta = 10 x 4 x 1/2 = 20 J.
Detailed Explanation: This question tests work by constant force. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
32. NEET Exam-style Question: A 2 kg body moves with speed 5 m/s. Its kinetic energy is: A 10 J B 25 J C 50 J D 100 J
Correct Answer: B. K = 1/2 mv2 = 25 J.
Detailed Explanation: This question tests kinetic energy. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
33. NEET Exam-style Question: A machine does 600 J work in 20 s. Average power is: A 20 W B 30 W C 60 W D 120 W
Correct Answer: B. P = W/t = 30 W.
Detailed Explanation: This question tests power. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
34. NEET Exam-style Question: A spring k = 200 N/m is compressed by 0.10 m. Stored energy is: A 0.5 J B 1 J C 2 J D 10 J
Correct Answer: B. U = 1/2 kx2 = 1 J.
Detailed Explanation: This question tests spring energy. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
35. NEET Exam-style Question: A body falls freely from height h. Just before ground, speed is: A gh B sqrt(gh) C sqrt(2gh) D 2gh
Correct Answer: C. mgh = 1/2 mv2.
Detailed Explanation: This question tests conservation of energy. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
36. NEET Exam-style Question: Work done by friction is usually: A positive B negative C zero always D infinite
Correct Answer: B. Friction usually opposes displacement.
Detailed Explanation: This question tests frictional loss. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
37. NEET Exam-style Question: Area under force-displacement graph gives: A power B work C pressure D momentum
Correct Answer: B. Work = integral F dx.
Detailed Explanation: This question tests F-x graph. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
38. NEET Exam-style Question: A machine input is 500 J and useful output is 350 J. Efficiency is: A 35% B 50% C 70% D 100%
Correct Answer: C. eta = output/input = 0.70.
Detailed Explanation: This question tests efficiency. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
39. NEET Exam-style Question: Net work done on a body equals change in: A momentum B kinetic energy C force D power
Correct Answer: B. Wnet = Delta K.
Detailed Explanation: This question tests work-energy theorem. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
40. NEET Exam-style Question: In an inelastic collision, which is always conserved for an isolated system? A KE B momentum C speed D power
Correct Answer: B. Momentum is conserved; KE may be lost.
Detailed Explanation: This question tests collision energy. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
41. NEET Exam-style Question: A force of 10 N acts at 60 degrees to displacement 4 m. Work done is closest to: A 10 J B 20 J C 40 J D 80 J
Correct Answer: B. W = Fs cos theta = 10 x 4 x 1/2 = 20 J.
Detailed Explanation: This question tests work by constant force. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
42. NEET Exam-style Question: A 2 kg body moves with speed 5 m/s. Its kinetic energy is: A 10 J B 25 J C 50 J D 100 J
Correct Answer: B. K = 1/2 mv2 = 25 J.
Detailed Explanation: This question tests kinetic energy. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
43. NEET Exam-style Question: A machine does 600 J work in 20 s. Average power is: A 20 W B 30 W C 60 W D 120 W
Correct Answer: B. P = W/t = 30 W.
Detailed Explanation: This question tests power. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
44. NEET Exam-style Question: A spring k = 200 N/m is compressed by 0.10 m. Stored energy is: A 0.5 J B 1 J C 2 J D 10 J
Correct Answer: B. U = 1/2 kx2 = 1 J.
Detailed Explanation: This question tests spring energy. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
45. NEET Exam-style Question: A body falls freely from height h. Just before ground, speed is: A gh B sqrt(gh) C sqrt(2gh) D 2gh
Correct Answer: C. mgh = 1/2 mv2.
Detailed Explanation: This question tests conservation of energy. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
46. NEET Exam-style Question: Work done by friction is usually: A positive B negative C zero always D infinite
Correct Answer: B. Friction usually opposes displacement.
Detailed Explanation: This question tests frictional loss. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
47. NEET Exam-style Question: Area under force-displacement graph gives: A power B work C pressure D momentum
Correct Answer: B. Work = integral F dx.
Detailed Explanation: This question tests F-x graph. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
48. NEET Exam-style Question: A machine input is 500 J and useful output is 350 J. Efficiency is: A 35% B 50% C 70% D 100%
Correct Answer: C. eta = output/input = 0.70.
Detailed Explanation: This question tests efficiency. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
49. NEET Exam-style Question: Net work done on a body equals change in: A momentum B kinetic energy C force D power
Correct Answer: B. Wnet = Delta K.
Detailed Explanation: This question tests work-energy theorem. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
50. NEET Exam-style Question: In an inelastic collision, which is always conserved for an isolated system? A KE B momentum C speed D power
Correct Answer: B. Momentum is conserved; KE may be lost.
Detailed Explanation: This question tests collision energy. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
09

JEE Main PYQs

50 difficult JEE Main-style questions on formulas, graphs, springs, power and collisions.

1. JEE Main Exam-style Question: Force varies as F = 3x<sup>2</sup>. Work from x=0 to x=2 m is:
Correct Answer: W = integral 3x2 dx = x3 from 0 to 2 = 8 J.
Detailed Explanation: This question tests variable force. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
2. JEE Main Exam-style Question: A triangular F-x graph has base 6 m and height 20 N. Work done is:
Correct Answer: Area = 1/2 x 6 x 20 = 60 J.
Detailed Explanation: This question tests F-x graph. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
3. JEE Main Exam-style Question: A 2 kg particle speed changes from 3 m/s to 7 m/s. Net work is:
Correct Answer: Delta K = 1/2 x 2 x (49 - 9) = 40 J.
Detailed Explanation: This question tests work-energy theorem. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
4. JEE Main Exam-style Question: A block compresses a spring k = 800 N/m by 0.05 m. Maximum spring energy is:
Correct Answer: U = 1/2 kx2 = 1 J.
Detailed Explanation: This question tests spring system. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
5. JEE Main Exam-style Question: A vehicle needs tractive force 1200 N at 20 m/s. Power required is:
Correct Answer: P = Fv = 24000 W = 24 kW.
Detailed Explanation: This question tests power and velocity. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
6. JEE Main Exam-style Question: A pump lifts 100 kg water by 10 m in 5 s. Power is approximately:
Correct Answer: P = mgh/t = 100 x 9.8 x 10 / 5 = 1960 W.
Detailed Explanation: This question tests lifting power. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
7. JEE Main Exam-style Question: A 1 kg block moving 4 m/s stops by compressing a spring k = 200 N/m. Compression is:
Correct Answer: 1/2 mv2 = 1/2 kx2, x = sqrt(16/200) = 0.283 m.
Detailed Explanation: This question tests conservation with spring. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
8. JEE Main Exam-style Question: A 5 kg block slides 10 m with friction 4 N. Energy lost is:
Correct Answer: Loss = f s = 40 J.
Detailed Explanation: This question tests friction. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
9. JEE Main Exam-style Question: A motor of 2 kW output runs with 80% efficiency. Input power is:
Correct Answer: Pin = 2/0.8 = 2.5 kW.
Detailed Explanation: This question tests efficiency. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
10. JEE Main Exam-style Question: Two bodies stick after collision. Which equation is used during collision?
Correct Answer: Conserve momentum; do not conserve kinetic energy.
Detailed Explanation: This question tests collision energy loss. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
11. JEE Main Exam-style Question: Force varies as F = 3x<sup>2</sup>. Work from x=0 to x=2 m is:
Correct Answer: W = integral 3x2 dx = x3 from 0 to 2 = 8 J.
Detailed Explanation: This question tests variable force. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
12. JEE Main Exam-style Question: A triangular F-x graph has base 6 m and height 20 N. Work done is:
Correct Answer: Area = 1/2 x 6 x 20 = 60 J.
Detailed Explanation: This question tests F-x graph. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
13. JEE Main Exam-style Question: A 2 kg particle speed changes from 3 m/s to 7 m/s. Net work is:
Correct Answer: Delta K = 1/2 x 2 x (49 - 9) = 40 J.
Detailed Explanation: This question tests work-energy theorem. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
14. JEE Main Exam-style Question: A block compresses a spring k = 800 N/m by 0.05 m. Maximum spring energy is:
Correct Answer: U = 1/2 kx2 = 1 J.
Detailed Explanation: This question tests spring system. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
15. JEE Main Exam-style Question: A vehicle needs tractive force 1200 N at 20 m/s. Power required is:
Correct Answer: P = Fv = 24000 W = 24 kW.
Detailed Explanation: This question tests power and velocity. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
16. JEE Main Exam-style Question: A pump lifts 100 kg water by 10 m in 5 s. Power is approximately:
Correct Answer: P = mgh/t = 100 x 9.8 x 10 / 5 = 1960 W.
Detailed Explanation: This question tests lifting power. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
17. JEE Main Exam-style Question: A 1 kg block moving 4 m/s stops by compressing a spring k = 200 N/m. Compression is:
Correct Answer: 1/2 mv2 = 1/2 kx2, x = sqrt(16/200) = 0.283 m.
Detailed Explanation: This question tests conservation with spring. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
18. JEE Main Exam-style Question: A 5 kg block slides 10 m with friction 4 N. Energy lost is:
Correct Answer: Loss = f s = 40 J.
Detailed Explanation: This question tests friction. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
19. JEE Main Exam-style Question: A motor of 2 kW output runs with 80% efficiency. Input power is:
Correct Answer: Pin = 2/0.8 = 2.5 kW.
Detailed Explanation: This question tests efficiency. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
20. JEE Main Exam-style Question: Two bodies stick after collision. Which equation is used during collision?
Correct Answer: Conserve momentum; do not conserve kinetic energy.
Detailed Explanation: This question tests collision energy loss. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
21. JEE Main Exam-style Question: Force varies as F = 3x<sup>2</sup>. Work from x=0 to x=2 m is:
Correct Answer: W = integral 3x2 dx = x3 from 0 to 2 = 8 J.
Detailed Explanation: This question tests variable force. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
22. JEE Main Exam-style Question: A triangular F-x graph has base 6 m and height 20 N. Work done is:
Correct Answer: Area = 1/2 x 6 x 20 = 60 J.
Detailed Explanation: This question tests F-x graph. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
23. JEE Main Exam-style Question: A 2 kg particle speed changes from 3 m/s to 7 m/s. Net work is:
Correct Answer: Delta K = 1/2 x 2 x (49 - 9) = 40 J.
Detailed Explanation: This question tests work-energy theorem. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
24. JEE Main Exam-style Question: A block compresses a spring k = 800 N/m by 0.05 m. Maximum spring energy is:
Correct Answer: U = 1/2 kx2 = 1 J.
Detailed Explanation: This question tests spring system. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
25. JEE Main Exam-style Question: A vehicle needs tractive force 1200 N at 20 m/s. Power required is:
Correct Answer: P = Fv = 24000 W = 24 kW.
Detailed Explanation: This question tests power and velocity. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
26. JEE Main Exam-style Question: A pump lifts 100 kg water by 10 m in 5 s. Power is approximately:
Correct Answer: P = mgh/t = 100 x 9.8 x 10 / 5 = 1960 W.
Detailed Explanation: This question tests lifting power. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
27. JEE Main Exam-style Question: A 1 kg block moving 4 m/s stops by compressing a spring k = 200 N/m. Compression is:
Correct Answer: 1/2 mv2 = 1/2 kx2, x = sqrt(16/200) = 0.283 m.
Detailed Explanation: This question tests conservation with spring. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
28. JEE Main Exam-style Question: A 5 kg block slides 10 m with friction 4 N. Energy lost is:
Correct Answer: Loss = f s = 40 J.
Detailed Explanation: This question tests friction. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
29. JEE Main Exam-style Question: A motor of 2 kW output runs with 80% efficiency. Input power is:
Correct Answer: Pin = 2/0.8 = 2.5 kW.
Detailed Explanation: This question tests efficiency. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
30. JEE Main Exam-style Question: Two bodies stick after collision. Which equation is used during collision?
Correct Answer: Conserve momentum; do not conserve kinetic energy.
Detailed Explanation: This question tests collision energy loss. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
31. JEE Main Exam-style Question: Force varies as F = 3x<sup>2</sup>. Work from x=0 to x=2 m is:
Correct Answer: W = integral 3x2 dx = x3 from 0 to 2 = 8 J.
Detailed Explanation: This question tests variable force. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
32. JEE Main Exam-style Question: A triangular F-x graph has base 6 m and height 20 N. Work done is:
Correct Answer: Area = 1/2 x 6 x 20 = 60 J.
Detailed Explanation: This question tests F-x graph. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
33. JEE Main Exam-style Question: A 2 kg particle speed changes from 3 m/s to 7 m/s. Net work is:
Correct Answer: Delta K = 1/2 x 2 x (49 - 9) = 40 J.
Detailed Explanation: This question tests work-energy theorem. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
34. JEE Main Exam-style Question: A block compresses a spring k = 800 N/m by 0.05 m. Maximum spring energy is:
Correct Answer: U = 1/2 kx2 = 1 J.
Detailed Explanation: This question tests spring system. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
35. JEE Main Exam-style Question: A vehicle needs tractive force 1200 N at 20 m/s. Power required is:
Correct Answer: P = Fv = 24000 W = 24 kW.
Detailed Explanation: This question tests power and velocity. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
36. JEE Main Exam-style Question: A pump lifts 100 kg water by 10 m in 5 s. Power is approximately:
Correct Answer: P = mgh/t = 100 x 9.8 x 10 / 5 = 1960 W.
Detailed Explanation: This question tests lifting power. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
37. JEE Main Exam-style Question: A 1 kg block moving 4 m/s stops by compressing a spring k = 200 N/m. Compression is:
Correct Answer: 1/2 mv2 = 1/2 kx2, x = sqrt(16/200) = 0.283 m.
Detailed Explanation: This question tests conservation with spring. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
38. JEE Main Exam-style Question: A 5 kg block slides 10 m with friction 4 N. Energy lost is:
Correct Answer: Loss = f s = 40 J.
Detailed Explanation: This question tests friction. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
39. JEE Main Exam-style Question: A motor of 2 kW output runs with 80% efficiency. Input power is:
Correct Answer: Pin = 2/0.8 = 2.5 kW.
Detailed Explanation: This question tests efficiency. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
40. JEE Main Exam-style Question: Two bodies stick after collision. Which equation is used during collision?
Correct Answer: Conserve momentum; do not conserve kinetic energy.
Detailed Explanation: This question tests collision energy loss. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
41. JEE Main Exam-style Question: Force varies as F = 3x<sup>2</sup>. Work from x=0 to x=2 m is:
Correct Answer: W = integral 3x2 dx = x3 from 0 to 2 = 8 J.
Detailed Explanation: This question tests variable force. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
42. JEE Main Exam-style Question: A triangular F-x graph has base 6 m and height 20 N. Work done is:
Correct Answer: Area = 1/2 x 6 x 20 = 60 J.
Detailed Explanation: This question tests F-x graph. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
43. JEE Main Exam-style Question: A 2 kg particle speed changes from 3 m/s to 7 m/s. Net work is:
Correct Answer: Delta K = 1/2 x 2 x (49 - 9) = 40 J.
Detailed Explanation: This question tests work-energy theorem. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
44. JEE Main Exam-style Question: A block compresses a spring k = 800 N/m by 0.05 m. Maximum spring energy is:
Correct Answer: U = 1/2 kx2 = 1 J.
Detailed Explanation: This question tests spring system. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
45. JEE Main Exam-style Question: A vehicle needs tractive force 1200 N at 20 m/s. Power required is:
Correct Answer: P = Fv = 24000 W = 24 kW.
Detailed Explanation: This question tests power and velocity. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
46. JEE Main Exam-style Question: A pump lifts 100 kg water by 10 m in 5 s. Power is approximately:
Correct Answer: P = mgh/t = 100 x 9.8 x 10 / 5 = 1960 W.
Detailed Explanation: This question tests lifting power. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
47. JEE Main Exam-style Question: A 1 kg block moving 4 m/s stops by compressing a spring k = 200 N/m. Compression is:
Correct Answer: 1/2 mv2 = 1/2 kx2, x = sqrt(16/200) = 0.283 m.
Detailed Explanation: This question tests conservation with spring. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
48. JEE Main Exam-style Question: A 5 kg block slides 10 m with friction 4 N. Energy lost is:
Correct Answer: Loss = f s = 40 J.
Detailed Explanation: This question tests friction. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
49. JEE Main Exam-style Question: A motor of 2 kW output runs with 80% efficiency. Input power is:
Correct Answer: Pin = 2/0.8 = 2.5 kW.
Detailed Explanation: This question tests efficiency. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
50. JEE Main Exam-style Question: Two bodies stick after collision. Which equation is used during collision?
Correct Answer: Conserve momentum; do not conserve kinetic energy.
Detailed Explanation: This question tests collision energy loss. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
10

JEE Advanced PYQs

50 advanced questions with complete solution ideas.

1. JEE Advanced Exam-style Question: For F = ax + b, derive work from x1 to x2.
Correct Answer: W = integral (ax+b)dx = a(x22-x12)/2 + b(x2-x1).
Detailed Explanation: This question tests variable force integration. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
2. JEE Advanced Exam-style Question: A force F = kx + alpha x<sup>3</sup> compresses a system from 0 to A. Work stored is:
Correct Answer: U = 1/2 kA2 + 1/4 alpha A4.
Detailed Explanation: This question tests nonlinear spring. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
3. JEE Advanced Exam-style Question: A bead slides from height h on a smooth track. Speed at bottom?
Correct Answer: v = sqrt(2gh), independent of path.
Detailed Explanation: This question tests energy and circular motion. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
4. JEE Advanced Exam-style Question: For masses m1,m2 and approach speed u, energy loss in direct collision is:
Correct Answer: Loss = 1/2 mu(1-e2)u2, mu = m1m2/(m1+m2).
Detailed Explanation: This question tests collision with e. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
5. JEE Advanced Exam-style Question: If work done is W = at<sup>3</sup>, instantaneous power at t is:
Correct Answer: P = dW/dt = 3at2.
Detailed Explanation: This question tests power as rate. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
6. JEE Advanced Exam-style Question: A graph has positive area 30 J and negative area 12 J. Net work?
Correct Answer: Net work = 18 J.
Detailed Explanation: This question tests F-x graph with negative area. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
7. JEE Advanced Exam-style Question: A block descends height h with friction work fL. Final KE from rest is:
Correct Answer: K = mgh - fL.
Detailed Explanation: This question tests rough incline. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
8. JEE Advanced Exam-style Question: A mass m hits spring with speed v on smooth surface. Maximum compression?
Correct Answer: x = v sqrt(m/k).
Detailed Explanation: This question tests spring collision. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
9. JEE Advanced Exam-style Question: Two machines of efficiencies 80% and 75% act in series. Overall efficiency?
Correct Answer: eta = 0.8 x 0.75 = 0.60 = 60%.
Detailed Explanation: This question tests efficiency chain. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
10. JEE Advanced Exam-style Question: Force F = (2x i + 3y j) N moves particle from (0,0) to (a,b) along axes. Work?
Correct Answer: W = integral 2x dx + integral 3y dy = a2 + 3b2/2.
Detailed Explanation: This question tests 2D work. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
11. JEE Advanced Exam-style Question: For F = ax + b, derive work from x1 to x2.
Correct Answer: W = integral (ax+b)dx = a(x22-x12)/2 + b(x2-x1).
Detailed Explanation: This question tests variable force integration. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
12. JEE Advanced Exam-style Question: A force F = kx + alpha x<sup>3</sup> compresses a system from 0 to A. Work stored is:
Correct Answer: U = 1/2 kA2 + 1/4 alpha A4.
Detailed Explanation: This question tests nonlinear spring. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
13. JEE Advanced Exam-style Question: A bead slides from height h on a smooth track. Speed at bottom?
Correct Answer: v = sqrt(2gh), independent of path.
Detailed Explanation: This question tests energy and circular motion. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
14. JEE Advanced Exam-style Question: For masses m1,m2 and approach speed u, energy loss in direct collision is:
Correct Answer: Loss = 1/2 mu(1-e2)u2, mu = m1m2/(m1+m2).
Detailed Explanation: This question tests collision with e. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
15. JEE Advanced Exam-style Question: If work done is W = at<sup>3</sup>, instantaneous power at t is:
Correct Answer: P = dW/dt = 3at2.
Detailed Explanation: This question tests power as rate. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
16. JEE Advanced Exam-style Question: A graph has positive area 30 J and negative area 12 J. Net work?
Correct Answer: Net work = 18 J.
Detailed Explanation: This question tests F-x graph with negative area. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
17. JEE Advanced Exam-style Question: A block descends height h with friction work fL. Final KE from rest is:
Correct Answer: K = mgh - fL.
Detailed Explanation: This question tests rough incline. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
18. JEE Advanced Exam-style Question: A mass m hits spring with speed v on smooth surface. Maximum compression?
Correct Answer: x = v sqrt(m/k).
Detailed Explanation: This question tests spring collision. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
19. JEE Advanced Exam-style Question: Two machines of efficiencies 80% and 75% act in series. Overall efficiency?
Correct Answer: eta = 0.8 x 0.75 = 0.60 = 60%.
Detailed Explanation: This question tests efficiency chain. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
20. JEE Advanced Exam-style Question: Force F = (2x i + 3y j) N moves particle from (0,0) to (a,b) along axes. Work?
Correct Answer: W = integral 2x dx + integral 3y dy = a2 + 3b2/2.
Detailed Explanation: This question tests 2D work. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
21. JEE Advanced Exam-style Question: For F = ax + b, derive work from x1 to x2.
Correct Answer: W = integral (ax+b)dx = a(x22-x12)/2 + b(x2-x1).
Detailed Explanation: This question tests variable force integration. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
22. JEE Advanced Exam-style Question: A force F = kx + alpha x<sup>3</sup> compresses a system from 0 to A. Work stored is:
Correct Answer: U = 1/2 kA2 + 1/4 alpha A4.
Detailed Explanation: This question tests nonlinear spring. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
23. JEE Advanced Exam-style Question: A bead slides from height h on a smooth track. Speed at bottom?
Correct Answer: v = sqrt(2gh), independent of path.
Detailed Explanation: This question tests energy and circular motion. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
24. JEE Advanced Exam-style Question: For masses m1,m2 and approach speed u, energy loss in direct collision is:
Correct Answer: Loss = 1/2 mu(1-e2)u2, mu = m1m2/(m1+m2).
Detailed Explanation: This question tests collision with e. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
25. JEE Advanced Exam-style Question: If work done is W = at<sup>3</sup>, instantaneous power at t is:
Correct Answer: P = dW/dt = 3at2.
Detailed Explanation: This question tests power as rate. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
26. JEE Advanced Exam-style Question: A graph has positive area 30 J and negative area 12 J. Net work?
Correct Answer: Net work = 18 J.
Detailed Explanation: This question tests F-x graph with negative area. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
27. JEE Advanced Exam-style Question: A block descends height h with friction work fL. Final KE from rest is:
Correct Answer: K = mgh - fL.
Detailed Explanation: This question tests rough incline. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
28. JEE Advanced Exam-style Question: A mass m hits spring with speed v on smooth surface. Maximum compression?
Correct Answer: x = v sqrt(m/k).
Detailed Explanation: This question tests spring collision. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
29. JEE Advanced Exam-style Question: Two machines of efficiencies 80% and 75% act in series. Overall efficiency?
Correct Answer: eta = 0.8 x 0.75 = 0.60 = 60%.
Detailed Explanation: This question tests efficiency chain. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
30. JEE Advanced Exam-style Question: Force F = (2x i + 3y j) N moves particle from (0,0) to (a,b) along axes. Work?
Correct Answer: W = integral 2x dx + integral 3y dy = a2 + 3b2/2.
Detailed Explanation: This question tests 2D work. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
31. JEE Advanced Exam-style Question: For F = ax + b, derive work from x1 to x2.
Correct Answer: W = integral (ax+b)dx = a(x22-x12)/2 + b(x2-x1).
Detailed Explanation: This question tests variable force integration. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
32. JEE Advanced Exam-style Question: A force F = kx + alpha x<sup>3</sup> compresses a system from 0 to A. Work stored is:
Correct Answer: U = 1/2 kA2 + 1/4 alpha A4.
Detailed Explanation: This question tests nonlinear spring. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
33. JEE Advanced Exam-style Question: A bead slides from height h on a smooth track. Speed at bottom?
Correct Answer: v = sqrt(2gh), independent of path.
Detailed Explanation: This question tests energy and circular motion. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
34. JEE Advanced Exam-style Question: For masses m1,m2 and approach speed u, energy loss in direct collision is:
Correct Answer: Loss = 1/2 mu(1-e2)u2, mu = m1m2/(m1+m2).
Detailed Explanation: This question tests collision with e. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
35. JEE Advanced Exam-style Question: If work done is W = at<sup>3</sup>, instantaneous power at t is:
Correct Answer: P = dW/dt = 3at2.
Detailed Explanation: This question tests power as rate. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
36. JEE Advanced Exam-style Question: A graph has positive area 30 J and negative area 12 J. Net work?
Correct Answer: Net work = 18 J.
Detailed Explanation: This question tests F-x graph with negative area. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
37. JEE Advanced Exam-style Question: A block descends height h with friction work fL. Final KE from rest is:
Correct Answer: K = mgh - fL.
Detailed Explanation: This question tests rough incline. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
38. JEE Advanced Exam-style Question: A mass m hits spring with speed v on smooth surface. Maximum compression?
Correct Answer: x = v sqrt(m/k).
Detailed Explanation: This question tests spring collision. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
39. JEE Advanced Exam-style Question: Two machines of efficiencies 80% and 75% act in series. Overall efficiency?
Correct Answer: eta = 0.8 x 0.75 = 0.60 = 60%.
Detailed Explanation: This question tests efficiency chain. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
40. JEE Advanced Exam-style Question: Force F = (2x i + 3y j) N moves particle from (0,0) to (a,b) along axes. Work?
Correct Answer: W = integral 2x dx + integral 3y dy = a2 + 3b2/2.
Detailed Explanation: This question tests 2D work. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
41. JEE Advanced Exam-style Question: For F = ax + b, derive work from x1 to x2.
Correct Answer: W = integral (ax+b)dx = a(x22-x12)/2 + b(x2-x1).
Detailed Explanation: This question tests variable force integration. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
42. JEE Advanced Exam-style Question: A force F = kx + alpha x<sup>3</sup> compresses a system from 0 to A. Work stored is:
Correct Answer: U = 1/2 kA2 + 1/4 alpha A4.
Detailed Explanation: This question tests nonlinear spring. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
43. JEE Advanced Exam-style Question: A bead slides from height h on a smooth track. Speed at bottom?
Correct Answer: v = sqrt(2gh), independent of path.
Detailed Explanation: This question tests energy and circular motion. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
44. JEE Advanced Exam-style Question: For masses m1,m2 and approach speed u, energy loss in direct collision is:
Correct Answer: Loss = 1/2 mu(1-e2)u2, mu = m1m2/(m1+m2).
Detailed Explanation: This question tests collision with e. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
45. JEE Advanced Exam-style Question: If work done is W = at<sup>3</sup>, instantaneous power at t is:
Correct Answer: P = dW/dt = 3at2.
Detailed Explanation: This question tests power as rate. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
46. JEE Advanced Exam-style Question: A graph has positive area 30 J and negative area 12 J. Net work?
Correct Answer: Net work = 18 J.
Detailed Explanation: This question tests F-x graph with negative area. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
47. JEE Advanced Exam-style Question: A block descends height h with friction work fL. Final KE from rest is:
Correct Answer: K = mgh - fL.
Detailed Explanation: This question tests rough incline. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
48. JEE Advanced Exam-style Question: A mass m hits spring with speed v on smooth surface. Maximum compression?
Correct Answer: x = v sqrt(m/k).
Detailed Explanation: This question tests spring collision. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
49. JEE Advanced Exam-style Question: Two machines of efficiencies 80% and 75% act in series. Overall efficiency?
Correct Answer: eta = 0.8 x 0.75 = 0.60 = 60%.
Detailed Explanation: This question tests efficiency chain. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
50. JEE Advanced Exam-style Question: Force F = (2x i + 3y j) N moves particle from (0,0) to (a,b) along axes. Work?
Correct Answer: W = integral 2x dx + integral 3y dy = a2 + 3b2/2.
Detailed Explanation: This question tests 2D work. Write the known quantities, choose the matching formula, keep SI units, and check whether work-energy theorem, conservation of energy, or power relation is the shortest route.
11

IB Questions

25 IB Physics questions with answers and explanations.

IB 1. Define work done by a force.
Work is energy transferred by a force through displacement: W = Fs cos theta.
IB 2. Explain why work is scalar.
It is the scalar dot product of force and displacement.
IB 3. State the work-energy theorem.
Net work done equals change in kinetic energy.
IB 4. A 4 kg mass moves at 3 m/s. Find KE.
K = 18 J.
IB 5. What is conservative force?
A force whose work is path independent and can be linked to potential energy.
IB 6. Give an example of non-conservative force.
Friction; it dissipates mechanical energy.
IB 7. Define power.
Rate of doing work or energy transfer.
IB 8. Unit of power?
Watt, equal to joule per second.
IB 9. State efficiency formula.
eta = useful output energy or power / input energy or power.
IB 10. Why is area under F-x graph work?
Because W = integral F dx.
IB 11. Spring energy formula.
U = 1/2 kx2.
IB 12. Ball dropped from height h, speed before ground.
v = sqrt(2gh).
IB 13. What happens to KE in inelastic collision?
Some kinetic energy changes to heat, sound and deformation.
IB 14. Work done by centripetal force in uniform circular motion?
Zero because force is perpendicular to displacement.
IB 15. Why does braking distance increase with speed?
Initial KE is proportional to v2.
IB 16. Calculate power for 100 J in 5 s.
20 W.
IB 17. What is horsepower?
1 HP = 746 W approximately.
IB 18. Meaning of negative work.
Force has component opposite displacement.
IB 19. Meaning of zero work.
Force is perpendicular to displacement or displacement is zero.
IB 20. Mechanical energy expression.
E = K + U.
IB 21. When is K+U constant?
When only conservative forces do work.
IB 22. Work by gravity going up height h.
-mgh for upward displacement.
IB 23. Work by gravity coming down height h.
+mgh.
IB 24. Power of vehicle at constant speed.
P = Fv against resistive force.
IB 25. Why machines have efficiency less than 100%?
Energy is lost to heat, sound and deformation.
12

IGCSE Questions

25 IGCSE Physics questions with direct answers.

IGCSE 1. Formula for work done.
W = force x distance in direction of force.
IGCSE 2. Unit of work.
Joule.
IGCSE 3. Formula for kinetic energy.
KE = 1/2 mv2.
IGCSE 4. Formula for gravitational potential energy.
GPE = mgh.
IGCSE 5. Formula for power.
P = E/t or W/t.
IGCSE 6. A 10 N force moves object 3 m. Work?
30 J if force is along displacement.
IGCSE 7. A 2 kg object at 4 m/s has KE?
16 J.
IGCSE 8. A 5 kg object raised by 2 m has GPE?
About 100 J using g=10 m/s2.
IGCSE 9. What is efficiency?
Useful output divided by total input.
IGCSE 10. Energy wasted in machines becomes?
Mostly thermal energy and sound.
IGCSE 11. Work done when force is perpendicular?
Zero.
IGCSE 12. What is renewable hydroelectric energy based on?
Gravitational potential energy of water.
IGCSE 13. Brakes convert kinetic energy into?
Thermal energy.
IGCSE 14. Unit of power.
Watt.
IGCSE 15. 1 kW equals?
1000 W.
IGCSE 16. A machine outputs 60 J from 100 J input. Efficiency?
60%.
IGCSE 17. Work done by friction is positive or negative?
Usually negative for moving object.
IGCSE 18. Energy cannot be?
Created or destroyed; it changes form.
IGCSE 19. Power tells how quickly energy is?
Transferred.
IGCSE 20. A heavier car at same speed has more?
Kinetic energy.
IGCSE 21. Doubling speed changes KE by factor?
Four.
IGCSE 22. Lifting same mass higher requires more?
Work/energy.
IGCSE 23. Work done if displacement is zero?
Zero.
IGCSE 24. Falling object loses GPE and gains?
KE.
IGCSE 25. Why use seatbelts?
They increase stopping time and reduce force.
13

A-Level Questions

25 A-Level questions with explanations.

A-Level 1. Derive work from variable force.
W = integral F dx along the path.
A-Level 2. Show dimensions of energy.
[ML2T-2].
A-Level 3. Show dimensions of power.
[ML2T-3].
A-Level 4. Work done by spring force from 0 to x.
-1/2 kx2 by spring; stored energy is +1/2 kx2.
A-Level 5. Terminal velocity power balance.
Driving or gravitational power equals resistive power.
A-Level 6. Conservative force relation.
F = -dU/dx in one dimension.
A-Level 7. Escape-like energy condition.
Use total mechanical energy conservation.
A-Level 8. Work by friction on rough horizontal surface.
-mu mg s.
A-Level 9. Spring plus gravity energy equation.
1/2 mv2 + mgh + 1/2 kx2 = constant if no loss.
A-Level 10. Power from force vector.
P = F dot v.
A-Level 11. Average power definition.
Total work divided by total time.
A-Level 12. Instantaneous power definition.
dW/dt.
A-Level 13. Energy loss in collision.
1/2 mu(1-e2)urel2.
A-Level 14. Coefficient of restitution.
Relative speed of separation / relative speed of approach.
A-Level 15. Elastic collision energy statement.
Total kinetic energy is conserved.
A-Level 16. Perfectly inelastic collision statement.
Bodies move together after collision.
A-Level 17. Work done by normal reaction on fixed smooth surface.
Zero.
A-Level 18. Area under P-t graph.
Energy transferred.
A-Level 19. Area under F-x graph.
Work done.
A-Level 20. Work in circular motion by tangential force.
Equals change in kinetic energy.
A-Level 21. Why dot product in work?
Only displacement-parallel force component transfers energy.
A-Level 22. Efficiency using power.
eta = useful output power/input power.
A-Level 23. Braking distance relation if braking force constant.
s proportional to v2.
A-Level 24. Work by gravity path dependence?
Independent of path, depends on height change.
A-Level 25. Non-conservative work relation.
Wnoncons = Delta(K+U).
14

Assertion Reason

30 assertion-reason questions on work, energy, power, springs, collisions and efficiency.

1. Assertion: Work is zero when force is perpendicular to displacement. Reason: Work is the dot product of force and displacement.
Both true; reason explains assertion.
2. Assertion: Net work changes kinetic energy. Reason: Work-energy theorem states Wnet = Delta K.
Both true; reason explains assertion.
3. Assertion: Friction usually decreases mechanical energy. Reason: Friction is a non-conservative force.
Both true; reason explains assertion.
4. Assertion: Spring potential energy is proportional to x squared. Reason: Spring force is proportional to x.
Both true; integration gives 1/2 kx squared.
5. Assertion: Power can be written as F dot v. Reason: Power is rate of work.
Both true; P=dW/dt=F dot dx/dt.
6. Assertion: Efficiency can exceed 100% in ordinary machines. Reason: Energy is conserved.
Assertion false; reason true.
7. Assertion: In elastic collision KE is conserved. Reason: Coefficient of restitution is 1.
Both true for ideal direct elastic collision.
8. Assertion: In inelastic collision momentum is not conserved. Reason: Kinetic energy is lost.
Assertion false; reason often true for isolated inelastic collision.
9. Assertion: Area under F-x graph gives work. Reason: Small work element is F dx.
Both true.
10. Assertion: A faster body has much larger kinetic energy. Reason: KE varies as v squared.
Both true.
11. Assertion: Work is zero when force is perpendicular to displacement. Reason: Work is the dot product of force and displacement.
Both true; reason explains assertion.
12. Assertion: Net work changes kinetic energy. Reason: Work-energy theorem states Wnet = Delta K.
Both true; reason explains assertion.
13. Assertion: Friction usually decreases mechanical energy. Reason: Friction is a non-conservative force.
Both true; reason explains assertion.
14. Assertion: Spring potential energy is proportional to x squared. Reason: Spring force is proportional to x.
Both true; integration gives 1/2 kx squared.
15. Assertion: Power can be written as F dot v. Reason: Power is rate of work.
Both true; P=dW/dt=F dot dx/dt.
16. Assertion: Efficiency can exceed 100% in ordinary machines. Reason: Energy is conserved.
Assertion false; reason true.
17. Assertion: In elastic collision KE is conserved. Reason: Coefficient of restitution is 1.
Both true for ideal direct elastic collision.
18. Assertion: In inelastic collision momentum is not conserved. Reason: Kinetic energy is lost.
Assertion false; reason often true for isolated inelastic collision.
19. Assertion: Area under F-x graph gives work. Reason: Small work element is F dx.
Both true.
20. Assertion: A faster body has much larger kinetic energy. Reason: KE varies as v squared.
Both true.
21. Assertion: Work is zero when force is perpendicular to displacement. Reason: Work is the dot product of force and displacement.
Both true; reason explains assertion.
22. Assertion: Net work changes kinetic energy. Reason: Work-energy theorem states Wnet = Delta K.
Both true; reason explains assertion.
23. Assertion: Friction usually decreases mechanical energy. Reason: Friction is a non-conservative force.
Both true; reason explains assertion.
24. Assertion: Spring potential energy is proportional to x squared. Reason: Spring force is proportional to x.
Both true; integration gives 1/2 kx squared.
25. Assertion: Power can be written as F dot v. Reason: Power is rate of work.
Both true; P=dW/dt=F dot dx/dt.
26. Assertion: Efficiency can exceed 100% in ordinary machines. Reason: Energy is conserved.
Assertion false; reason true.
27. Assertion: In elastic collision KE is conserved. Reason: Coefficient of restitution is 1.
Both true for ideal direct elastic collision.
28. Assertion: In inelastic collision momentum is not conserved. Reason: Kinetic energy is lost.
Assertion false; reason often true for isolated inelastic collision.
29. Assertion: Area under F-x graph gives work. Reason: Small work element is F dx.
Both true.
30. Assertion: A faster body has much larger kinetic energy. Reason: KE varies as v squared.
Both true.
15

Case Study Questions

Passage-based cases with 4-5 questions, answers and detailed explanations.

Roller coaster: Passage and Questions
Passage: A car starts from rest at height h and moves on a nearly smooth track. Questions: find speed at bottom, identify energy conversion, effect of friction, condition for loop, and why mass cancels.
Answers and Detailed Explanation: Use mgh = 1/2 mv2. Speed = sqrt(2gh) on a smooth track. GPE converts to KE. Friction reduces speed. Loop condition needs sufficient speed at top.
Spring compression: Passage and Questions
Passage: A block of mass m moving with speed v compresses spring k. Questions: maximum compression, energy stored, role of friction, graph area, and rebound speed.
Answers and Detailed Explanation: Smooth case: 1/2 mv2 = 1/2 kx2. With friction, subtract f x. Spring graph area is triangular.
Car braking: Passage and Questions
Passage: A car of mass m at speed v is stopped by constant braking force F. Questions: braking distance, heat produced, speed doubled effect, work by brakes, and safety lesson.
Answers and Detailed Explanation: F s = 1/2 mv2. Distance is proportional to v2. Brakes do negative work and convert KE into heat.
Lift power: Passage and Questions
Passage: A lift raises total mass M through height h in time t. Questions: useful work, power, efficiency, motor input, and effect of speed.
Answers and Detailed Explanation: Useful work = Mgh. Useful power = Mgh/t. Input power = useful power/eta.
Collisions: Passage and Questions
Passage: Two carts collide and stick together. Questions: common speed, KE loss, conserved quantity, why KE fails, and energy forms after collision.
Answers and Detailed Explanation: Use momentum for common speed. KE loss becomes heat, sound and deformation.
Hydroelectric conversion: Passage and Questions
Passage: Water falls from height h at mass flow rate r. Questions: available power, turbine output, efficiency, units, and energy chain.
Answers and Detailed Explanation: Available power = rgh. Output = eta rgh. GPE becomes KE then electrical energy.
Work by friction: Passage and Questions
Passage: A block slides on a rough horizontal surface. Questions: work by friction, energy loss, stopping distance, dependence on speed, and sign convention.
Answers and Detailed Explanation: Friction work = -mu mg s. Stopping distance from mu mg s = 1/2 mv2.
16

Quick Revision Notes

Final compact checklist before exam.

Most Important Formulas

  • W = Fs cos theta
  • W = ∫F dx
  • K = 1/2mv2
  • U = mgh and 1/2kx2
  • P = W/t = Fv

Graph Areas

  • Area under F-x = work
  • Area under P-t = energy
  • Slope of U-x gives -F
  • Positive and negative areas cancel algebraically

NEET Shortcuts

  • Use energy for speed after height change
  • Use Wnet = Delta K for force-distance
  • For constant speed, net work is zero
  • Efficiency always less than 1 for ordinary machines

JEE Traps

  • Variable force requires integration
  • Friction path length matters
  • Spring force is not constant
  • Collision KE is not always conserved

Common Mistakes

  • Forgetting cos theta
  • Using kg instead of newton
  • Mixing work and power
  • Using fake KE conservation in inelastic collision

Units and Checklist

  • Work/Energy: joule
  • Power: watt
  • Efficiency: no unit
  • Dimension of energy: ML2T-2
  • Check signs before final answer

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