IIT PHASE–2 (Advanced) – PART VI
Very Tough IIT Problems

This section contains high-difficulty IIT-JEE Advanced problems that decide ranks. These problems require energy balance, constraint handling, and calm judgment.

Problem 1: Variable Friction + Energy

Question:
A block of mass m moves on a horizontal surface where the coefficient of friction varies with position as μ = kx. If the block starts with speed u at x = 0, find the distance it travels before stopping.

Strategy:

Use work–energy theorem. Friction force varies with x.

Energy balance:

Initial KE = Work done by friction

½mu² = ∫₀ˢ (kx · mg) dx

½mu² = mgk (s² / 2)

Answer:

s = u / √(gk)

IIT Insight: Equations of motion are useless here.

Problem 2: Energy + Moving Pulley (Advanced)

Question:
A light pulley of mass M hangs from the ceiling. A light string passes over it carrying masses m₁ and m₂. Find the speed of the system after descending height h.

Key Difficulty:

• Pulley has kinetic energy
• Rotational + translational energy involved

Energy balance:

Loss in PE = KE of m₁ + KE of m₂ + KE of pulley

IIT Note: Such problems test awareness of hidden energy terms.

Problem 3: Energy + Elastic Collision

Question:
A particle of mass m moving with speed u collides elastically with a stationary particle of mass 2m. Find the loss of kinetic energy of the first particle.

Method:

• Use momentum conservation
• Use kinetic energy conservation

Advanced Insight: Energy is conserved globally, but redistributed locally.

Problem 4: Potential Well + Turning Points

Question:
A particle moves in a one-dimensional potential U(x) = ax⁴ − bx². Determine the nature of motion for different values of total energy.

Concept:

• Turning points from E = U(x)
• Bounded and unbounded motion

IIT Level: Conceptual + graphical understanding required.

Problem 5: Energy + Sudden Loss

Question:
A particle moving with speed v suddenly loses half of its kinetic energy. Find the ratio of final speed to initial speed.

Solution:

KE ∝ v² → v₂² = ½v₁²

Answer:

v₂ / v₁ = 1 / √2

IIT Trap: Many students incorrectly take v₂ = v₁ / 2.

Problem 6: Energy + Constraint Geometry

Question:
A particle slides down a smooth track whose shape is arbitrary. Show that its speed at a given vertical depth depends only on the depth.

Reasoning:

Only gravity does work → energy conserved.

Classic IIT Insight: Path independence of conservative forces.

Phase–2 Tough Problem Discipline

• Do not panic if solution is not immediate
• Write energy balance clearly
• Expect hidden energy terms
• Trust conservation laws

“These problems separate qualifiers from rankers.”

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.

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📚 Complete Lesson Index (Part 1 – Part 39)

1. Part 1 – Introduction to Work
2. Part 2 – Types of Work
3. Part 3 – Variable Force & Graphs
4. Part 4 – Kinetic Energy
5. Part 5 – Work–Energy Theorem
6. Part 6 – Potential Energy
7. Part 7 – Conservative Forces
8. Part 8 – Mechanical Energy
9. Part 9 – Power
10. Part 10 – Power Applications
11. Part 11
12. Part 12
13. Part 13
14. Part 14
15. Part 15
16. Part 16
17. Part 17
18. Part 18
19. Part 19
20. Part 20
21. Part 21
22. Part 22
23. Part 23
24. Part 24
25. Part 25
26. Part 26
27. Part 27
28. Part 28
29. Part 29
30. Part 30
31. Part 31
32. Part 32
33. Part 33
34. Part 34
35. Part 35
36. Part 36
37. Part 37
38. Part 38
39. Part 39 – Final IIT Tough Problems & Solutions

Prepared by: Shaktimatha Learning 🌱

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