IIT PHASE–2 (Advanced) – PART IV
Ultra-Tough Mixed Problems

This part contains selection-level IIT problems where multiple concepts act together. These questions are not formula-based; they test judgment, sequencing, and calm execution.

Problem 1: Energy + Friction + Variable Motion

Question:
A block of mass m is projected up a rough incline with initial speed u. The coefficient of friction is μ and angle of inclination is θ. Find the total distance travelled before the block comes to rest.

Step 1: Forces doing work

• Gravity → conservative
• Friction → non-conservative

Step 2: Energy balance

Initial KE = Work against gravity + Work against friction

½mu² = mg(s sinθ) + μmg(s cosθ)

Step 3: Solve for distance

s = u² / [2g (sinθ + μcosθ)]

IIT Insight: Direction does not matter — only total energy loss matters.

Problem 2: Energy + Constraint (Moving Wedge)

Question:
A block slides down a smooth wedge which is free to move on a smooth floor. Find the speed of the block when it reaches the bottom.

Key IIT Difficulty:

• Two bodies moving
• No external horizontal force

Strategy:

• Use conservation of mechanical energy
• Use momentum conservation horizontally (constraint)

Topper move: Never try to find acceleration of wedge.

Problem 3: Energy + Circular Motion + Constraint

Question:
A particle enters a vertical circular track. Determine the minimum speed at the bottom so that it does not lose contact at the top.

Critical condition at top:

Normal reaction = 0 → v² = gR

Energy equation:

½mv₀² = mg(2R) + ½m(gR)

Answer:

v₀ = √(5gR)

IIT Trick: First apply force condition, then energy.

Problem 4: Energy + Potential Well (Advanced)

Question:
A particle moves in a one-dimensional potential well U(x). Explain how turning points are determined.

Core Rule:

Turning point occurs when KE = 0 → Total Energy = Potential Energy

Advanced Insight:

• Force may be non-zero at turning point
• Motion depends on energy inequality, not force direction

Problem 5: Energy Loss + Multiple Segments

Question:
A particle moves on a track having smooth and rough sections. How is final speed determined?

Correct Approach:

• Break motion into segments
• Apply energy balance separately
• Subtract energy loss only in rough sections

IIT Insight: Energy loss is local, not global.

Phase–2 Execution Rules (VERY IMPORTANT)

• Do not mix laws randomly
• Respect constraints (rope, wedge, pulley)
• Energy first, force later
• Never panic when equations look less

“Advanced IIT problems are about control, not complexity.”

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 🌱

Strong Concepts • Smart Practice • Exam Success