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).

📐

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 ↗

Ready to attempt under real exam pressure?

Test your speed and accuracy in the authentic 200-minute timed NTA simulator.

Launch NEET 2023 CBT Test →

← Previous (Q.10) All Physics Questions Grid Next (Q.12) →

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

⚖️ Legal & Fair Dealing Notice: Sourced from publicly released NEET 2023 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 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?

🔗 Related Questions — Work, Energy and Power

Work Done by a Linearly Variable Friction Force on a Moving Slab

1D Elastic Collision of Equal Masses and Maximum Height Rise of Pendulum Bob

Stopping Distance, Retarding Force & Kinetic Energy Ratio

String Slack Condition in Upper Half of Vertical Circle

Solve 4 NEET Questions a Day — One per Subject