MIND GROW Magazine

Properties of Matter – Stage 2 (Page 6)

IIT-JEE Advanced PYQs • Concept Integration • Error Control

1. IIT Advanced PYQ: Composite Wire Stretch

Question Pattern:
Two wires of equal length but different Young’s moduli are joined in series and stretched by force F.

Solution Logic:

Force remains same in both wires
Extension depends on Y and A

ΔL = (FL/Y₁A) + (FL/Y₂A)

Exam Trap:
Assuming equal extension instead of equal force.

2. PYQ: Rod with Linearly Varying Area

Given:
Radius varies as r = r₀(1 + x/L)

Correct Approach:

Express area as function of x
Use differential extension
Integrate over full length

IIT Expectation:
Integration skill + physical interpretation.

3. PYQ: Elastic Energy Comparison

Two wires stretched to same extension but made of different materials.

Key Insight:

Elastic Energy ∝ YA

Trap:
Energy does NOT depend on length if extension is fixed.

4. PYQ: Breaking of Wire with Hanging Mass

Wire breaks under its own weight.

Hidden Concept:

Maximum stress at top
Use differential element approach

σ_max = ρgL

Advanced Insight:
Breaking may occur without any external load.

5. PYQ: Thermal Stress + Elasticity

Rod fixed at both ends, temperature raised.

Result:

σ = YαΔT

No expansion allowed
Internal force generated

Exam Mistake:
Assuming expansion happens even when rod is fixed.

6. PYQ: Combination of Springs & Wires

Spring attached to wire, system pulled by force.

Method:

Same force in series
Total extension = spring + wire extension

ΔL = F/k + FL/(YA)

7. PYQ Speed-Solving Strategy

Check dimensions instantly
Use proportional reasoning
Apply extreme limits (Y → ∞, A → 0)

Stage 2 – Page 6 Takeaways

Real IIT-Advanced patterns decoded
Integration-based elasticity mastered
Thermal stress clarity achieved
Common traps eliminated

Stage 2 – Page 6 Completed ✅
Next → Stage 2 – Page 7 (Tough Mixed Concept Numericals)

📘 Properties of Matter – Complete Physics Library (IIT-JEE)

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.