MIND GROW Magazine

Properties of Matter – Stage 2 (Page 3)

Mixed Concept Problems & PYQ Patterns (IIT-JEE)

1. PYQ Pattern: Elasticity + Energy

Problem Type:
A wire is stretched by force F within elastic limit. Find ratio of elastic energy stored to work done by force.

Elastic Energy = (1/2) × Work Done

IIT Insight:
This result is valid only for linear stress–strain region.

2. Mixed Concept: Elasticity + Gravity

Problem:
A wire of length L and area A hangs vertically under its own weight. Find total elongation.

ΔL = (ρ g L²) / (2Y)

JEE Trap:
Do NOT use F = mg at bottom directly; force varies along length.

3. PYQ Pattern: Elasticity + Thermal Stress

Problem:
A rod is heated and partially constrained. Find final stress.

σ = Y(αΔT − strain allowed)

Key Skill:
Subtract free expansion from actual extension.

4. Conceptual PYQ: Young’s Modulus Logic

Question:
Which material stretches more under same force and dimensions?

Lower Young’s modulus → more extension
Higher Young’s modulus → stiffer material

Common Mistake:
Confusing strength with stiffness.

5. Multi-Concept: Elastic Rod + Spring System

Problem:
A spring and wire are connected in series. Find effective spring constant.

1 / k_eq = 1 / k + L / (Y A)

IIT Level:
Elastic rod behaves like a spring.

6. Assertion–Reason PYQ Pattern

Assertion: Steel is preferred over rubber for bridges.
Reason: Steel has higher Young’s modulus.

Correct Answer:

Assertion: True
Reason: True
Reason correctly explains assertion

7. Order of Magnitude PYQs

Typical values to remember:

Young’s modulus of steel ≈ 2 × 10¹¹ N/m²
Breaking strain ≈ 10⁻²
Elastic strain limit ≈ 10⁻³

JEE Trick:
Eliminate options using magnitude.

8. How IIT Frames Elasticity Questions

Combine elasticity with mechanics
Focus on constraints & boundary conditions
Prefer conceptual elimination
Use graphs stress vs strain

Stage 2 – Page 3 Summary

PYQ logic mastered
Mixed concept numericals
Thermal + elastic coupling
Assertion–Reason clarity

Stage 2 – Page 3 Completed ✅
Next: Stage 2 – Page 4 (High-Level Traps & Advanced MCQs)

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