IIT TOUGH PROBLEMS – SET 3
Work, Energy & Power
This set contains very high-difficulty IIT-Advanced problems. These questions demand deep reasoning, patience, and correct sequencing. Do not attempt them in a hurry.
Problem 1: Energy + Two Variable Forces
Question:
A particle of mass m moves along the x-axis under two forces:
F₁ = kx and F₂ = −bx².
If the particle starts from rest at x = 0, find its speed at position x = a.
Strategy:
- Both forces are position-dependent
- Acceleration is not constant
Energy method:
Change in KE = Work done by net force
½mv² = ∫₀ᵃ (kx − bx²) dx
½mv² = (ka²/2) − (ba³/3)
Answer:
v = √[(ka² − 2ba³/3)/m]
IIT Insight: Never try F = ma when force depends on x.
Problem 2: Energy + Constraint + Friction
Question:
A block slides down a rough wedge which itself rests on a rough horizontal floor.
Explain how energy analysis must be modified to find final speed.
Key difficulty:
- Two bodies moving
- Energy lost at two contact points
Correct thinking:
- Energy is NOT conserved
- Work done by friction at both surfaces must be included
IIT Insight: Energy loss can occur at multiple interfaces simultaneously.
Problem 3: Energy + Non-Uniform Gravity
Question:
A particle moves vertically where gravitational acceleration varies with height as
g(h) = g₀(1 − h/H).
Find the work done by gravity when the particle moves from h = 0 to h = H/2.
Method:
Work = ∫ F dh = ∫ mg(h) dh
W = m ∫₀ᴴ⁄₂ g₀(1 − h/H) dh
W = mg₀ [h − h²/(2H)]₀ᴴ⁄₂
Answer:
W = (3/8) mg₀H
IIT Level: Combines calculus with physical interpretation.
Problem 4: Energy + Sudden Constraint Change
Question:
A particle moving on a smooth surface suddenly encounters a rigid constraint
that changes its direction without changing speed.
Explain the energy change.
Analysis:
- Constraint force acts
- Force is perpendicular to velocity
Conclusion:
No work is done → kinetic energy remains unchanged.
Key Concept: Direction change ≠ energy change.
Problem 5: Energy Bound & Accessibility
Question:
A particle has total mechanical energy E and moves in a potential U(x).
Derive the condition for regions where motion is forbidden.
Energy principle:
KE = E − U(x)
Condition:
- If E ≥ U(x) → motion possible
- If E < U(x) → motion forbidden
IIT Insight: Motion is decided by energy inequality, not force.
Problem 6: Energy + Scaling Argument
Question:
If the speed of a particle is increased by 20%, find the percentage increase
in its kinetic energy.
Logic:
KE ∝ v²
New KE ∝ (1.2v)² = 1.44v²
Answer:
Percentage increase = 44%
IIT Trap: Many students answer 20% incorrectly.
How to Use Tough Set-3
- Attempt only after Phase-2 basics
- Do not time yourself initially
- Focus on reasoning, not speed
- Re-solve after 24 hours
“If these problems feel hard, you are on the right path.”
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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