IIT TOUGH PROBLEMS – SET 4
Work, Energy & Power
This set contains extreme-difficulty IIT-Advanced problems. These questions test energy inequalities, hidden work, constraint logic, and non-obvious method selection. Attempt only after mastering Sets 1–3.
Problem 1: Energy Inequality + Turning Points
Question:
A particle of mass m moves in a one-dimensional potential
U(x) = U₀(1 − x²/a²).
For what range of total energy E is the motion bounded?
Find the turning points.
Key idea:
Motion is possible only when E ≥ U(x).
Turning points:
E = U₀(1 − x²/a²)
x = ±a√(1 − E/U₀)
IIT Insight: Bounded motion comes from energy inequality, not force direction.
Problem 2: Energy + Two-Stage Friction Loss
Question:
A block slides down a smooth incline and then moves on a rough horizontal surface
with coefficient of friction μ.
Find the total distance travelled before stopping.
Correct approach:
- Energy conserved on incline
- Energy lost only on rough surface
Energy flow:
mgh = Work done by friction = μmg s
Answer:
s = h / μ
Trap: Many students incorrectly include friction on incline.
Problem 3: Energy + Moving Reference Frame
Question:
A block slides on a smooth wedge which itself moves with constant velocity.
Determine whether the kinetic energy of the block changes.
Analysis:
- No friction
- No work by constraint force
Conclusion:
Kinetic energy of the block remains unchanged.
Advanced Idea: Energy change is frame-independent when no work is done.
Problem 4: Energy + Gradually Applied Force
Question:
A force F is gradually increased from 0 to F₀ while moving a particle through
distance s. Compare the work done with Fs.
Key concept:
Work = Area under F–x graph
Result:
Work < F₀s
IIT Insight: Average force matters, not maximum force.
Problem 5: Energy + Explosion with Constraint
Question:
A block at rest on a smooth surface explodes into two fragments
which remain connected by a spring.
Describe the energy transformation.
Key laws:
- Momentum conserved
- Mechanical energy not conserved
Advanced Insight: Internal energy converts to KE + spring PE.
Problem 6: Energy + Path Independence Proof
Question:
Prove that the work done by gravity between two points
is independent of the path taken.
Reasoning:
- Gravitational force is conservative
- Work depends only on vertical displacement
IIT Standard: This result underlies all height-based shortcuts.
Problem 7: Energy + Maximum Compression (Advanced)
Question:
A block slides down an incline and compresses a spring placed at the bottom.
Find the maximum compression considering gravity during compression.
Energy balance:
Initial KE + PE = Spring PE + Work against gravity
Trap: Ignoring gravity during compression gives wrong answer.
Work, Energy & Power – Complete Physics Library
This is the MASTER LIBRARY PAGE for the complete chapter Work, Energy and Power, prepared for Intermediate, IIT-JEE (Main & Advanced), NEET and competitive exams.
All concepts are explained from basic to IIT level, including theory, derivations, numerical problems, objective questions, previous year questions, tough IIT problems, tricks and cautions.
📚 Complete Lesson Index (Part 1 – Part 39)
- Part 1 – Introduction to Work
- Part 2 – Types of Work
- Part 3 – Variable Force & Graphs
- Part 4 – Kinetic Energy
- Part 5 – Work–Energy Theorem
- Part 6 – Potential Energy
- Part 7 – Conservative Forces
- Part 8 – Mechanical Energy
- Part 9 – Power
- Part 10 – Power Applications
- Part 11
- Part 12
- Part 13
- Part 14
- Part 15
- Part 16
- Part 17
- Part 18
- Part 19
- Part 20
- Part 21
- Part 22
- Part 23
- Part 24
- Part 25
- Part 26
- Part 27
- Part 28
- Part 29
- Part 30
- Part 31
- Part 32
- Part 33
- Part 34
- Part 35
- Part 36
- Part 37
- Part 38
- Part 39 – Final IIT Tough Problems & Solutions
Prepared by: Shaktimatha Learning 🌱
Strong Concepts • Smart Practice • Exam Success
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