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:

✓

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

⚡

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)].

🛡️

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

📐

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.

⭐

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)].

💡

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

⚠️

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).

📖

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 ↗

Ready to attempt under real exam pressure?

Test your speed and accuracy in the authentic 180-minute timed NTA simulator.

Launch NEET 2020 CBT Test →

← Previous (Q.160) All Physics Questions Grid Next (Q.162) →

Spotted a mistake in this solution? Report an error (support@mycompetitiveexams.com)

⚖️ Legal & Fair Dealing Notice: Sourced from publicly released NEET 2020 question papers and NEET answer keys for private study, research, and non-commercial educational practice under Fair Dealing (Section 52(1)(a) of the Indian Copyright Act, 1957). Not affiliated with or endorsed by NTA or NMC.

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?

🔗 Related Questions — Mechanical Properties of Solids

Maximum Elastic Elongation of a Steel Wire

Longitudinal Stress Induced by Suspended Load

Solve 4 NEET Questions a Day — One per Subject