Q.11 Physics ⭐ 360° Option Elimination Active

NEET 2023 Physics Question 11 Solution

Topic: Work, Energy and Power · Official NTA Booklet Code G5

Question

The potential energy of a long spring when stretched by 2 cm is U. If the spring is stretched by 8 cm, potential energy stored in it will be:

✓

Verified Against NTA Final Answer Key

Option (1) : 16U

📚 Work, Energy and Power Easy

📋 Given Parameters & Problem Setup

Initial Stretch (x₁) 2 cm

Initial Potential Energy (U₁) U

Final Stretch (x₂) 8 cm

⚡

The 30-Second Exam Hall Shortcut: ⚡ Quadratic Displacement Scaling Factor

⏱️ Save ~30 seconds

Potential energy scales with the square of stretch (U ∝ x²)! 8 cm is 4 times 2 cm, so energy is 4² × U = 16U in 5 seconds!

1 Elastic potential energy formula: U = (1/2) k x².

2 Notice that spring constant k is unchanged, so U ∝ x².

3 Find the stretch ratio: x₂ / x₁ = 8 cm / 2 cm = 4.

4 Square the stretch ratio: (4)² = 16.

5 New potential energy U₂ = 16 U. Immediately select Option (1)!

🛡️

Why You Can 100% Trust This Shortcut: Fundamental Work-Energy Principles · Elastic Potential Energy (Hooke's law quadratic integration: U = 1/2 k x² ∝ x²).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Elastic Potential Energy Formula

The work done against the restoring spring force F = -kx in stretching a spring of spring constant k by displacement x is stored as elastic potential energy:

U = \int_{0}^{x} k x \, dx = \frac{1}{2} k x^2

Step 2

Initial and Final Energy Expressions

Write expressions for initial state x₁ = 2 cm and final state x₂ = 8 cm:

U_1 = \frac{1}{2} k (2)^2 = 2k = U, \qquad U_2 = \frac{1}{2} k (8)^2 = 32k

Step 3

Ratio Evaluation

Take the ratio of final to initial potential energy:

\frac{U_2}{U_1} = \left(\frac{x_2}{x_1}\right)^2 = \left(\frac{8}{2}\right)^2 = 4^2 = 16 \implies U_2 = 16 U

⭐

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)

✓ 100% Correct

Verdict & Scientific Reason:

Accurate value: energy scales with square of stretch (4² = 16).

💡

Why this is airtight: None. Candidate correctly applied quadratic displacement scaling.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Underestimates energy by a factor of 8.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate took the ratio 8 - 2 = 6 or confused with half-powers.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Linear scaling error.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate treated potential energy as linearly proportional to displacement (U ∝ x, so 8/2 = 4U) instead of quadratic (U ∝ x²).

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

Arbitrary linear/power confusion.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate multiplied 4 by 2 instead of squaring 4.

⚠️

NTA Trap Alert: Linear vs Quadratic Scaling Trap (Picking 4U)

The most popular distractor is Option (3) 4U. Hasty students think "stretch is 4 times, so energy is 4 times", forgetting the square in (1/2)kx².

🛡️ How to avoid the -1 mark: Always repeat mentally: Spring energy is QUADRATIC in displacement: U ∝ x².

📖

Core NEET Syllabus Standard

National Eligibility cum Entrance Test (NEET UG) · Work, Energy and Power Standard Benchmark

Core Scientific Principle Tested:

"Spring restoring force is linear (F = -kx), making the stored potential energy strictly quadratic (U = 1/2 k x²)."

Syllabus Focus: Potential Energy of a Spring and Conservative Forces

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Physics Question 11 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Quadratic Displacement Scaling Factor

Step-by-Step Rigorous Workflow & Mathematical Proof

Elastic Potential Energy Formula

Initial and Final Energy Expressions

Ratio Evaluation

360° Option Elimination Engine Key Feature

NTA Trap Alert: Linear vs Quadratic Scaling Trap (Picking 4U)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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