Q.161 Physics ⭐ 360° Option Elimination Active

NEET 2020 Physics Question 161 Solution

Topic: Mechanical Properties of Solids · Official NTA Booklet Code E1

Question

A wire of length L, area of cross section A is hanging from a fixed support. The length of the wire changes to L₁ when mass M is suspended from its free end. The expression for Young's modulus is:

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Verified Against NTA Final Answer Key

Option (4) : MgL / [A(L1 - L)]

📚 Mechanical Properties of Solids Easy

📋 Given Parameters & Problem Setup

Initial Length L

Cross-sectional Area A

Suspended Mass M

Stretched Length L1

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The 30-Second Exam Hall Shortcut: ⚡ "Y = Stress / Strain = (Mg/A) / ((L1 - L)/L) = MgL / [A(L1 - L)]!"

⏱️ 20 seconds

Young's modulus is defined as longitudinal stress divided by longitudinal strain. Stress = Mg/A and strain = (L1 - L)/L. Combining gives Y = MgL / [A(L1 - L)]. Spot elongation ΔL = (L1 - L) in the denominator to identify Option (4) instantly!

1 Identify stretching force: F = Mg.

2 Elongation: ΔL = L1 - L.

3 Longitudinal strain: ε = ΔL / L = (L1 - L) / L.

4 Longitudinal stress: σ = F / A = Mg / A.

5 Young's modulus: Y = σ / ε = [Mg / A] / [(L1 - L) / L] = MgL / [A(L1 - L)].

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Why You Can 100% Trust This Shortcut: NCERT Physics · Mechanical Properties of Solids (Young's Modulus Formulation)

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Define Longitudinal Stress

When mass $M$ is suspended from the free end, the deforming tensile force acting across the cross-sectional area $A$ of the wire is its weight: $F = Mg$ $\text{Longitudinal Stress} = \frac{F}{A} = \frac{Mg}{A}$ .

Step 2

Define Longitudinal Strain

The initial length of the wire is $L$ , and the stretched final length is $L_1$ . Change in length (elongation): $\Delta L = L_1 - L$ $\text{Longitudinal Strain} = \frac{\Delta L}{L} = \frac{L_1 - L}{L}$ .

Step 3

Combine into Young’s Modulus Formula

Young's modulus ( $Y$ ) is defined as the ratio of longitudinal stress to longitudinal strain within the elastic limit: $Y = \frac{\text{Stress}}{\text{Strain}} = \frac{\frac{Mg}{A}}{\frac{L_1 - L}{L}}$ .

Step 4

Algebraic Simplification

Inverting the denominator fraction yields: $Y = \frac{Mg \cdot L}{A(L_1 - L)}$ . Matches Option 4.

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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 A

✗ Incorrect

Verdict & Scientific Reason:

Incorrect; substitutes final length L1 instead of change in length ΔL = L1 - L in the denominator.

⚠️

Student Fallacy (Why candidates pick this trap): Confusing final length with elongation.

2 B

✗ Incorrect

Verdict & Scientific Reason:

Incorrect; inverts the strain term, putting elongation in the numerator.

⚠️

Student Fallacy (Why candidates pick this trap): Inverting the fractional strain expression.

3 C

✗ Incorrect

Verdict & Scientific Reason:

Incorrect; would yield Y = Mg/A as if strain were equal to 1.

⚠️

Student Fallacy (Why candidates pick this trap): Cancelling lengths without accounting for elongation.

4 D

✓ 100% Correct

Verdict & Scientific Reason:

Accurate expression; Y = (Mg/A) / ((L1 - L)/L) = MgL / [A(L1 - L)].

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Why this is airtight: None; textbook definition of Young’s modulus.

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NTA Trap Alert: Strain vs Elongation

Strain is fractional change in length (ΔL / L = (L1 - L) / L). Writing strain as L1 / L is a fatal mistake.

🛡️ How to avoid the -1 mark: Always check that the denominator contains elongation ΔL = (L1 - L).

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Core NEET Syllabus Standard

Physics · Mechanical Properties of Solids Standard Benchmark

Core Scientific Principle Tested:

Syllabus Focus: Young's Modulus of a Hanging Wire under Suspended Mass

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2020 Physics Question 161 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ "Y = Stress / Strain = (Mg/A) / ((L1 - L)/L) = MgL / [A(L1 - L)]!"

Step-by-Step Rigorous Workflow & Mathematical Proof

Define Longitudinal Stress

Define Longitudinal Strain

Combine into Young’s Modulus Formula

Algebraic Simplification

360° Option Elimination Engine Key Feature

NTA Trap Alert: Strain vs Elongation

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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