Q.13 Physics · Section A ⭐ 360° Option Elimination Active

NEET 2024 Physics Question 13 Solution

Topic: System of Particles and Rotational Motion · Official NTA Booklet Code T1

Question

The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is 2400 g cm². The length of the 400 g rod is nearly:

✓

Verified Against NTA Final Answer Key

Option (3) : 8.5 cm

📚 System of Particles and Rotational Motion Easy

📋 Given Parameters & Problem Setup

Moment of inertia about central transverse axis I = 2400 g cm²

Mass of the thin rod M = 400 g

⚡

The 30-Second Exam Hall Shortcut: ⚡ Standard Rod Formula Inversion

⏱️ Save ~40 seconds

I = ML² / 12 -> L² = 12 I / M = 12 × 2400 / 400 = 12 × 6 = 72 -> L = √72 ≈ 8.485 cm ≈ 8.5 cm!

1 Central moment of inertia of a thin rod: I = (1/12) M L².

2 Rearrange for L²: L² = 12 I / M.

3 Substitute: L² = 12 × 2400 / 400 = 12 × 6 = 72 cm².

4 Take square root: L = √72 = √(36 × 2) = 6√2 = 6 × 1.414 = 8.485 cm ≈ 8.5 cm.

5 Option (3) is matched in under 15 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Standard Moment of Inertia of a Thin Uniform Rod (I_cm = (1/12) M L²).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formula for Moment of Inertia of a Uniform Rod

For a uniform thin straight rod of mass M and length L, the moment of inertia about an axis perpendicular to the rod and passing through its center of mass (midpoint) is given by integration as:

I = \frac{1}{12} M L^2

Step 2

Substitution of Given Physical Parameters

Substituting the given values I = 2400 g cm² and M = 400 g directly into the formula (in CGS units):

2400 = \frac{1}{12} (400) L^2

Step 3

Algebraic Simplification for L²

Simplifying the equation:

2400 = \frac{100}{3} L^2 \implies L^2 = \frac{2400 \times 3}{100} = 24 \times 3 = 72\,\text{cm}^2

Step 4

Square Root Evaluation

Taking the square root of 72:

L = \sqrt{72} = \sqrt{36 \times 2} = 6 \sqrt{2} \approx 6 \times 1.4142 = 8.485\,\text{cm} \approx 8.5\,\text{cm}

⭐

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:

Incorrect; would occur if formula for rod about one end (I = ML²/3) was used with incorrect algebra.

⚠️

Student Fallacy (Why candidates pick this trap): Using end-axis formula ML²/3 or miscalculating square root.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Confuses L² (72 cm²) with L (8.5 cm), forgetting to take the square root!

⚠️

Student Fallacy (Why candidates pick this trap): Stopping at L² = 72 and picking 72 cm directly.

3 (3)

✓ 100% Correct

Verdict & Scientific Reason:

Exact root of L² = 72 cm²: L = 8.485 cm ≈ 8.5 cm.

💡

Why this is airtight: None.

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

Approximately double the correct length.

⚠️

Student Fallacy (Why candidates pick this trap): Confusing half-length with full length.

⚠️

NTA Trap Alert: Forgetting the Square Root (L² vs L)

NTA intentionally included 72.0 cm as Option (2) because students calculate L² = 72 and instinctively bubble it without taking the square root.

🛡️ How to avoid the -1 mark: Always check units and ask yourself: is this value L or L²?

📖

Core NEET Syllabus Standard

Physics Core Mechanics · System of Particles and Rotational Motion Standard Benchmark

Core Scientific Principle Tested:

"The moment of inertia of a uniform rod of mass M and length L about its central transverse axis is I = ML²/12."

Syllabus Focus: Moment of Inertia of Standard Bodies

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Through the Center divide by 12; Square root of 72 is 8.5!

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NEET 2024 Physics Question 13 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Standard Rod Formula Inversion

Step-by-Step Rigorous Workflow & Mathematical Proof

Formula for Moment of Inertia of a Uniform Rod

Substitution of Given Physical Parameters

Algebraic Simplification for L²

Square Root Evaluation

360° Option Elimination Engine Key Feature

NTA Trap Alert: Forgetting the Square Root (L² vs L)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — System of Particles and Rotational Motion

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