MIND GROW Magazine

Properties of Matter – Stage 3 (Page 2)

JEE Advanced PYQs • Hidden Traps • Examiner Thinking

1. PYQ-Type: Energy Stored in Deformation

Question Pattern:

A wire of length L and cross-section A is stretched by force F. Find energy stored.

IIT Thinking:

Elastic energy is NOT kinetic
Depends on stress & strain
Area under stress–strain curve

Correct Expression:

U = (1/2) × stress × strain × volume

Trap:
Many students use (1/2)kx² directly → wrong for rods.

2. Advanced Trap: Same Stress ≠ Same Elongation

Two rods have same stress applied.

Different lengths
Different areas

Key Result:

Stress same
Strain same
Elongation different

Golden Rule:
Strain is material property response, elongation is geometry dependent.

3. PYQ-Type: Composite Rod (Series)

Rod A + Rod B joined end to end

Same force acts on both
Stress different
Total elongation = sum

Total Extension:

ΔL = (F L₁)/(A₁ Y₁) + (F L₂)/(A₂ Y₂)

IIT Trick:
Never average Young’s modulus in series.

4. Composite Rod (Parallel) – Killer Concept

Key Differences:

Elongation same
Force divides
Stress different

Force Ratio:

F₁/F₂ = (A₁Y₁)/(A₂Y₂)

Advanced Insight:
Stiffer material takes more force.

5. Poisson’s Ratio – IIT Favourite Logic

μ = lateral strain / longitudinal strain

μ < 0.5 → solid
μ = 0.5 → incompressible
μ > 0.5 → impossible

Direct Elimination:
Any option with μ > 0.5 is wrong.

6. Thermal Stress – Advanced Level

Rod fixed between rigid supports.

Temperature increases by ΔT

Free expansion prevented
Stress develops internally

Stress:

σ = Y α ΔT

Common Mistake:
Students subtract mechanical strain unnecessarily.

7. Graph-Based PYQs

Slope → modulus
Area → energy density
Breaking stress ≠ elastic limit

Examiner Trick:
Graph labels are intentionally small – read carefully.

Stage 3 – Thinking Upgrade

Never assume proportionality blindly
Check geometry vs material
Stress ≠ force
Strain ≠ elongation

Stage 3 Page 2 Completed ✔
Next → Stage 3 Page 3 (Tough PYQs + Multi-Step Reasoning)

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This library provides a complete, exam-oriented coverage of Properties of Matter for Class XI, IIT-JEE Main & JEE Advanced, including theory, numericals, applications, and advanced problem-solving.