Q.11 Physics · Section A ⭐ 360° Option Elimination Active

NEET 2024 Physics Question 11 Solution

Topic: Mechanical Properties of Solids · Official NTA Booklet Code T1

Question

The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young's modulus, respectively, are 8×10⁸ N m⁻² and 2×10¹¹ N m⁻², is:

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Verified Against NTA Final Answer Key

Option (3) : 4 mm

📚 Mechanical Properties of Solids Easy

📋 Given Parameters & Problem Setup

Length of steel wire L = 1 m

Elastic limit (maximum allowable stress) σ_max = 8 × 10⁸ N m⁻²

Young’s modulus of steel Y = 2 × 10¹¹ N m⁻²

⚡

The 30-Second Exam Hall Shortcut: ⚡ Hooke’s Law Direct Substitution

⏱️ Save ~40 seconds

ΔL_max = (σ_max / Y) × L = (8 × 10⁸ / 2 × 10¹¹) × 1 = 4 × 10⁻³ m = 4 mm!

1 Young’s modulus definition: Y = Stress / Strain = σ / (ΔL / L).

2 Rearrange for maximum elongation: ΔL = (σ / Y) × L.

3 Substitute: ΔL = (8 × 10⁸ / 2 × 10¹¹) × 1 = 4 × 10⁻³ m.

4 Convert to millimeters: 4 × 10⁻³ m = 4 mm.

5 Option (3) is solved in under 10 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Hooke’s Law & Definition of Young’s Modulus (Y = Stress / Strain).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Definition of Elastic Limit and Hooke’s Law

Up to the elastic limit, deformation is completely reversible, and Hooke’s law holds rigorously. Young’s modulus Y is defined as the ratio of tensile stress σ to tensile strain ε:

Y = \frac{\sigma}{\varepsilon} = \frac{\sigma}{\Delta L / L}

Step 2

Formulation for Maximum Elongation

To find the maximum elongation ΔL_max without exceeding the elastic limit, we use the maximum allowable stress σ_max:

\Delta L_{max} = \frac{\sigma_{max} \cdot L}{Y}

Step 3

Numerical Calculation

Substituting σ_max = 8 × 10⁸ N m⁻², L = 1 m, and Y = 2 × 10¹¹ N m⁻²:

\Delta L_{max} = \frac{(8 \times 10^8\,\text{N m}^{-2})(1\,\text{m})}{2 \times 10^{11}\,\text{N m}^{-2}} = 4 \times 10^{-3}\,\text{m}

Step 4

Unit Conversion to Millimeters

Since 1 m = 1000 mm:

\Delta L_{max} = 4 \times 10^{-3} \times 10^3\,\text{mm} = 4\,\text{mm}

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 (1)

✗ Incorrect

Verdict & Scientific Reason:

Off by a factor of 10.

⚠️

Student Fallacy (Why candidates pick this trap): Dividing powers of ten incorrectly (10⁸ / 10¹¹ as 10⁻² instead of 10⁻³).

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Fails to divide by the factor of 2 in Young’s modulus.

⚠️

Student Fallacy (Why candidates pick this trap): Using Y = 1 × 10¹¹ N/m².

3 (3)

✓ 100% Correct

Verdict & Scientific Reason:

Accurate evaluation: ΔL = 4 × 10⁻³ m = 4 mm.

💡

Why this is airtight: None.

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

Off by a factor of 10.

⚠️

Student Fallacy (Why candidates pick this trap): Unit conversion slip from meters to millimeters.

⚠️

NTA Trap Alert: Power of Ten Metric Conversion Slip

Students frequently mix up 10⁻³ m as 0.4 mm or 40 mm when rushing.

🛡️ How to avoid the -1 mark: 10⁻³ m is precisely 1 millimeter. Therefore, 4 × 10⁻³ m = 4 mm.

📖

Core NEET Syllabus Standard

Physics Core Properties of Matter · Mechanical Properties of Solids Standard Benchmark

Core Scientific Principle Tested:

"Tensile strain is the ratio of tensile stress to Young’s modulus (ΔL/L = σ/Y)."

Syllabus Focus: Elastic Moduli and Hooke’s Law

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Stress over Y times Length: 8/2 gives 4, 10⁻³ makes it mm!

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NEET 2024 Physics Question 11 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Hooke’s Law Direct Substitution

Step-by-Step Rigorous Workflow & Mathematical Proof

Definition of Elastic Limit and Hooke’s Law

Formulation for Maximum Elongation

Numerical Calculation

Unit Conversion to Millimeters

360° Option Elimination Engine Key Feature

NTA Trap Alert: Power of Ten Metric Conversion Slip

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Mechanical Properties of Solids

Longitudinal Stress Induced by Suspended Load

Young's Modulus of a Hanging Wire under Suspended Mass

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