IIT PHASE–2 (Advanced) – PART II Advanced Solved Problems
This section contains advanced IIT-level problems where energy methods alone are insufficient. Students must intelligently combine energy, force constraints, and logic.
Problem 1: Block + Rough Surface + Energy Loss
Question:
A block of mass m slides down a rough incline of angle θ with coefficient
of friction μ. Find its speed after moving a distance s.
Step 1: Identify forces
- Gravity → conservative
- Friction → non-conservative
Step 2: Energy balance
Initial KE + PE − Work by friction = Final KE
0 + mg(s sinθ) − (μmg cosθ)s = ½ mv²
Step 3: Simplify
v² = 2gs (sinθ − μcosθ)
Answer:
v = √[2gs (sinθ − μcosθ)]
IIT Insight: Acceleration never needed.
Problem 2: Pulley System (Constraint + Energy)
Question:
Two blocks of masses m and 2m are connected by a light string over
a smooth pulley. Find the speed after the system moves distance h.
Step 1: Constraint
- Both blocks have same speed magnitude
Step 2: Energy change
- 2m moves down → loses PE = 2mgh
- m moves up → gains PE = mgh
Net energy gain:
ΔE = mgh
Step 3: KE of system
½ mv² + ½ (2m)v² = 3/2 mv²
Final equation:
mgh = 3/2 mv²
Answer:
v = √(2gh/3)
Topper move: Avoid tension & acceleration completely.
Problem 3: Variable Force + Work-Energy
Question:
A particle moves under a force F = kx.
Find its speed when it moves from x = 0 to x = a.
Mass of particle is m.
Step 1: Work done
W = ∫₀ᵃ kx dx = ½ka²
Step 2: Work–energy theorem
½ka² = ½ mv²
Answer:
v = √(ka²/m)
Examiner trick: Acceleration is not constant → equations of motion fail.
Problem 4: Energy + Circular Motion
Question:
A particle slides down a smooth track and enters a vertical loop of radius R.
Find the minimum height from which it must start to complete the loop.
Step 1: Condition at top
- Minimum speed → N = 0
- v² = gR
Step 2: Energy balance
mgh = mg(2R) + ½m(gR)
Solve:
h = 5R/2
Answer:
Minimum height = 2.5R
Classic IIT favourite problem.
Problem 5: Energy as Inequality
Question:
A particle moves in a potential field U(x). Under what condition is motion possible?
Key condition:
Total Energy ≥ Potential Energy
Meaning:
- If E < U → motion impossible
- Turning points occur at E = U
Advanced idea: Motion limits are decided by energy, not forces.
Problem 6: Energy + Sudden Change
Question:
A moving particle suddenly experiences a loss of energy ΔE.
How does speed change?
Method:
- KE₁ = ½mv₁²
- KE₂ = KE₁ − ΔE
Answer:
v₂ = √(v₁² − 2ΔE/m)
IIT Application: Used in explosion & impact models.
Phase–2 Problem-Solving Discipline
- Never rush to equations
- Draw rough energy flow diagram
- Identify constraints early
- Break motion into stages
“Phase–2 problems reward patience and structure.”
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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