Q.19 Physics ⭐ 360° Option Elimination Active

NEET 2023 Physics Question 19 Solution

Topic: Mechanical Properties of Fluids · Official NTA Booklet Code G5

Question

The amount of energy required to form a soap bubble of radius 2 cm from a soap solution is nearly: (surface tension of soap solution = 0.03 N m⁻¹)

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Verified Against NTA Final Answer Key

Option (4) : 3.01 × 10⁻⁴ J

📚 Mechanical Properties of Fluids Medium

📋 Given Parameters & Problem Setup

Bubble Radius (r) 2 cm = 2 × 10⁻² m

Surface Tension (T) 0.03 N/m

Surface Structure Soap bubble (2 free surfaces: inner and outer)

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The 30-Second Exam Hall Shortcut: ⚡ The Factor of 2 Double-Surface Rule (W = 8πr²T)

⏱️ Save ~45 seconds

A soap bubble has TWO surfaces, so ΔA = 2 × (4πr²) = 8πr²! W = 8 × 3.14 × (4 × 10⁻⁴) × 0.03 ≈ 3.01 × 10⁻⁴ J in 25 seconds!

1 CRITICAL ALERT: A soap bubble in air has TWO surfaces (inner air-film interface and outer film-air interface).

2 Total surface area created: ΔA = 2 × (4π r²) = 8π r².

3 Substitute r = 2 × 10⁻² m: r² = 4 × 10⁻⁴ m².

4 Compute area: 8 × π × 4 × 10⁻⁴ = 32π × 10⁻⁴ ≈ 100.53 × 10⁻⁴ m².

5 Multiply by surface tension: W = T × ΔA = 0.03 × 100.53 × 10⁻⁴ ≈ 3.016 × 10⁻⁴ J.

6 Immediately match Option (4) 3.01 × 10⁻⁴ J!

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Why You Can 100% Trust This Shortcut: Fundamental Fluid Mechanics · Surface Energy (A hollow soap bubble in air has two liquid-gas interfaces: W = 2 × 4πr² T).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Two Free Surfaces of a Soap Bubble

Unlike a solid liquid drop which has only one outer surface, a soap bubble has a hollow spherical air pocket inside and air outside, creating two distinct liquid-air interfaces of virtually identical surface area:

A_{\text{total}} = 2 \times \left(4\pi r^2\right) = 8\pi r^2

Step 2

Work Done / Surface Energy Relation

The work done W required to form the bubble from a soap solution is equal to the surface energy created:

W = T \Delta A = T \left(8\pi r^2\right)

Step 3

Numerical Calculation

Substitute radius r = 2 × 10⁻² m and surface tension T = 0.03 N/m:

W = 0.03 \times 8 \times \pi \times (2 \times 10^{-2})^2 = 0.24\pi \times 4 \times 10^{-4} = 0.96 \pi \times 10^{-4}\text{ J}

Step 4

Decimal Precision Evaluation

Using π ≈ 3.1416:

W = 0.96 \times 3.1416 \times 10^{-4} = 3.0159 \times 10^{-4}\text{ J} \approx 3.01 \times 10^{-4}\text{ J}

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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 (1)

✗ Incorrect

Verdict & Scientific Reason:

Gross arithmetic error off by more than an order of magnitude.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate miscalculated powers of ten during metric conversion.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Off by a factor of 10 in decimal exponent (30.16 × 10⁻⁴ = 3.016 × 10⁻³ J).

⚠️

Student Fallacy (Why candidates pick this trap): Candidate misplaced the decimal point by taking 0.96 × π = 30.16 instead of 3.016.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Incorrect numerical coefficient.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate used wrong sphere volume or pressure formulas.

4 (4)

✓ 100% Correct

Verdict & Scientific Reason:

Accurate calculation accounting for both free surfaces: W = 8πr²T ≈ 3.01 × 10⁻⁴ J.

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Why this is airtight: None. Candidate correctly factored the two free surfaces of a soap bubble.

⚠️

NTA Trap Alert: Treating a Soap Bubble as a Single Surface Liquid Drop

A liquid drop has 1 surface (W = 4πr²T = 1.51 × 10⁻⁴ J). A soap bubble has 2 surfaces (W = 8πr²T = 3.01 × 10⁻⁴ J). Forgetting the factor of 2 is the #1 mistake in NEET surface tension questions.

🛡️ How to avoid the -1 mark: Rule: Liquid drop = 4πr²T. Soap bubble in air = 8πr²T.

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Core NEET Syllabus Standard

National Eligibility cum Entrance Test (NEET UG) · Mechanical Properties of Fluids Standard Benchmark

Core Scientific Principle Tested:

"Surface energy equals work done in creating free surface area: W = T ΔA. Soap bubbles possess two concentric interfaces."

Syllabus Focus: Surface Tension, Surface Energy, and Excess Pressure

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Physics Question 19 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ The Factor of 2 Double-Surface Rule (W = 8πr²T)

Step-by-Step Rigorous Workflow & Mathematical Proof

Two Free Surfaces of a Soap Bubble

Work Done / Surface Energy Relation

Numerical Calculation

Decimal Precision Evaluation

360° Option Elimination Engine Key Feature

NTA Trap Alert: Treating a Soap Bubble as a Single Surface Liquid Drop

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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