MIND GROW Magazine

Properties of Matter – Stage 2 (Page 9)

Extreme Traps • Multi-Statement Questions • JEE Advanced Logic

1. Multi-Statement Trap: Elastic Energy

Statements:

Elastic energy stored depends on applied force.
Elastic energy stored depends on extension.
Elastic energy stored depends on Young’s modulus.

Correct Thinking:

U = (1/2) F × ΔL = (F²L)/(2AY)

Statement 1 → True
Statement 2 → True
Statement 3 → True

IIT Trap:
Different forms hide same dependency.

2. Extreme Trap: Zero Lateral Strain?

A material stretched longitudinally shows no lateral contraction.

Inference:

Poisson’s ratio μ = 0
Material is cork-like

JEE Warning:
Do NOT assume all solids have μ ≈ 0.25.

3. Multi-Correct: Moduli Relationships

Which are always true?

Y = 2μ(1 + μ)
Y = 3B(1 − 2μ)
B = Y / [3(1 − 2μ)]
μ < 0.5 for stable solids

Correct Set:

✔ Y = 3B(1 − 2μ)
✔ B = Y / [3(1 − 2μ)]
✔ μ < 0.5

Examiner Trick:
Wrong equations look dimensionally correct.

4. Assertion–Reason: Stretching & Density

Assertion: Density of a stretched wire decreases.

Reason: Volume of the wire increases on stretching.

Truth Check:

Length ↑
Area ↓
Net volume ↑ slightly

Correct Option:
Both Assertion and Reason are true, and Reason explains Assertion.

5. Killer Trap: Same Stress, Different Strain

Two materials under same stress show different strain.

Key Relation:

Strain = Stress / Young’s Modulus

Higher Y → smaller strain
Lower Y → larger strain

IIT Mindset:
Never compare strain without comparing modulus.

6. Multi-Statement: Thermal + Mechanical Effects

Given: Rod heated and compressed simultaneously.

Net strain:

ε = αΔT − (σ / Y)

Thermal strain → expansion
Stress strain → contraction

Advanced Tip:
Signs decide final answer, not magnitude.

7. Ultimate Multi-Correct Trap: Breaking Condition

Select correct statements:

Breaking force ∝ area
Breaking stress independent of length
Breaking depends on Young’s modulus
Breaking stress is material property

Correct:

✔ Breaking force ∝ area
✔ Breaking stress is material property

Classic IIT Trap:
Young’s modulus does NOT decide breaking.

Stage 2 – Page 9 Summary

Extreme traps dismantled
Multi-statement logic mastered
Sign-based reasoning sharpened
Examiner mindset decoded

Stage 2 – Page 9 Completed ✅
Next → Stage 2 – Page 10 (Final Trap Compilation & Confidence Builder)

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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.