MIND GROW Magazine

Properties of Matter – Stage 3 (Page 5)

JEE Advanced Killer PYQs • Rank-Deciding Concepts • Final Traps

1. Wire + Pulley + Hanging Mass (Dynamic Elasticity)

A mass is suspended by a wire passing over a frictionless pulley.

Elite Thinking:

Tension is same throughout wire
Elongation occurs due to total tension
Pulley does NOT change stress

IIT Trap:
Many assume two tensions because two sides exist.

2. Rod Under Combined Thermal + Mechanical Load

Rod is stretched by force and heated simultaneously.

Total Strain:

ε = (σ / Y) + αΔT

Key Rule:

Mechanical strain → reversible
Thermal strain → independent of force

Exam Trick:
Forgetting to add strains algebraically.

3. PYQ: Minimum Radius to Avoid Breaking

Wire supports a mass, find minimum radius.

Correct Path:

Maximum stress ≤ breaking stress
σ = mg / A
Solve for radius

Warning:
Breaking stress ≠ Young’s modulus.

4. Series–Parallel Mixed Elastic System

Multiple wires arranged in mixed configuration.

Golden Rules:

Same force → series
Same elongation → parallel
Convert to equivalent spring

Shortcut:
Treat wires like springs only AFTER identifying geometry.

5. PYQ: Energy Lost in Sudden Loading

Load applied suddenly to a wire.

Key Result:

Energy lost = Elastic energy stored

Reason:

Work done by force = 2 × stored energy
Half is lost as internal vibrations

Topper Insight:
This is NOT collision energy loss.

6. Non-Uniform Cross-Section Rod

Radius varies along length.

Correct Method:

Take small element dx
Write local stress
Integrate elongation

IIT Trick:
Never use average area.

7. Stress–Strain Curve: Breaking vs Elastic Limit

Elastic limit < yield point < breaking point
Energy till elastic limit = recoverable
Beyond elastic limit = permanent loss

Exam Focus:
Questions often mix these three points.

FINAL IIT COMMANDMENTS

Always decide constraint first
Stress comes from force, strain from deformation
Thermal effects add, constraints subtract
Never trust symmetry blindly

Stage 3 – Page 5 COMPLETED ✔
You have finished Properties of Matter at IIT-Advanced Depth 🚀

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