MIND GROW Magazine

Properties of Matter – Stage 2 (Page 7)

Tough Mixed-Concept Problems • Advanced Tricks • Smart Shortcuts

1. PYQ Type: Elasticity + Gravity + Variable Cross-section

A vertical wire of length L has area varying with height. Find total elongation due to its own weight.

Correct IIT Approach:

Take a small element dx at height x
Force = weight of wire below x
Stress and strain vary continuously

d(ΔL) = (Force × dx)/(Y × A(x))

Shortcut:
If A(x) increases upward → elongation reduces drastically.

2. PYQ: Wire Breaking Under Combined Loads

A wire supports a mass and also has its own weight.

Key Principle:

Maximum stress occurs at topmost point
Total force = external load + weight of wire

σ_max = (Mg + ρALg)/A

Common IIT Trap:
Ignoring self-weight contribution.

3. PYQ: Elastic Energy Stored in Non-uniform Wire

Elastic energy density varies along the length.

Correct Method:

Compute local strain energy
Integrate over entire length

dU = (σ² / 2Y) × dV

IIT Level Insight:
Energy depends on stress distribution, not just total force.

4. PYQ: Bulk Modulus + Liquid Column

A liquid-filled vessel is subjected to pressure change.

Advanced Logic:

Pressure varies with depth
Volume compression is non-uniform

ΔV = ∫ (dP / B) × V

Exam Insight:
Uniform pressure formula fails for tall liquid columns.

5. PYQ: Poisson’s Ratio – Volume Change Trap

A rod is stretched longitudinally.

True Statement:

ΔV/V = (1 − 2μ) × longitudinal strain

If μ = 0.5 → volume remains constant
If μ < 0.5 → volume increases

JEE Trap:
Assuming volume always increases on stretching.

6. PYQ: Wire + Spring + Thermal Expansion

System has spring and wire fixed between rigid walls, temperature raised.

Correct Strategy:

Use compatibility of deformation
Force adjusts until equilibrium

YαΔT = σ + (σ / kL)

Advanced Tip:
Thermal stress distributes between spring and wire.

7. Rapid Elimination Tricks (JEE Advanced)

Check limiting cases (μ → 0.5, Y → ∞)
Use dimensional filtering
Estimate order of magnitude
Identify physically impossible options

Stage 2 – Page 7 Summary

Multi-concept integration mastered
Stress, energy, thermal effects unified
Advanced PYQ traps neutralized
Speed-based solving improved

Stage 2 – Page 7 Completed ✅
Next → Stage 2 – Page 8 (Gold-Level Conceptual & Assertion-Reason)

📘 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.