MIND GROW Magazine

Properties of Matter – Stage 2 (Page 5)

Advanced Numericals • PYQ Patterns • Calculation Control

1. IIT Advanced Numerical: Wire Under Load

Problem Type:
A wire of length L, area A, Young’s modulus Y is stretched by force F. Find elastic energy stored.

Elastic Energy = F²L / (2YA)

Trap:
Students wrongly use ½ kx² without converting k correctly.

2. PYQ Favorite: Variable Cross-Section Wire

Concept:
Wire whose radius varies along length.

IIT Method:

Divide wire into small elements dx
Use differential extension: dℓ = (F dx)/(Y A(x))
Integrate over full length

Topper Rule:
Never use average area unless explicitly stated.

3. Multi-Concept Numerical: Two Wires in Series

Given:
Two wires of different materials connected end to end.

Key Results:

Same force acts in both wires
Total extension = sum of individual extensions

ΔL = (FL₁)/(Y₁A₁) + (FL₂)/(Y₂A₂)

4. Two Wires in Parallel (High-Frequency IIT)

Important:

Extension same for both wires
Force divides according to stiffness

F₁ / F₂ = (Y₁A₁) / (Y₂A₂)

Common Mistake:
Assuming equal force in parallel connection.

5. Breaking Stress Numerical

Problem:
Find maximum extension before breaking.

σ_break = F_max / A

ΔL_max = (σ_break L) / Y

Trap:
Breaking stress ≠ elastic limit stress.

6. Temperature + Elasticity Numerical

Concept:
Wire heated while ends fixed.

Thermal Stress:

σ = Y α ΔT

Extension = 0
Stress generated internally

IIT Insight:
Most students forget force develops even without extension.

7. Extreme Case Technique (Numerical Elimination)

If Y → ∞ → no extension
If A → ∞ → no extension
If L → 0 → no extension

Usage:
Eliminate wrong options in seconds.

8. PYQ Speed Calculation Tips

Keep symbols till final step
Cancel before substitution
Never plug numbers early

Stage 2 – Page 5 Summary

Advanced numericals mastered
Series & parallel wire problems
Breaking stress clarity
Thermal stress confidence

Stage 2 – Page 5 Completed ✅
Next: Stage 2 – Page 6 (Previous Year IIT Advanced Problems)

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