Q.24 Physics ⭐ 360° Option Elimination Active

NEET 2026 Physics Question 24 Solution

Topic: Thermal Properties of Matter · Official NTA Booklet Code 50

Question

The temperature of a metallic sphere of radius R is increased by a small amount ΔT. If the linear coefficient of thermal expansion of the metal is α, the approximate increase in the volume of the sphere is:

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Verified Against NTA Final Answer Key

Option (3) : Delta V = 4 * pi * R^3 * alpha * Delta T

📚 Thermal Properties of Matter Easy

📋 Given Parameters & Problem Setup

Body Metallic sphere of radius R

Temperature Increase Small amount Delta T

Linear Expansion Coefficient alpha

Target Quantity Approximate increase in volume Delta V

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The 30-Second Exam Hall Shortcut: ⚡ Differential Volume Expansion Rule

⏱️ Eliminates memorization confusion.

Differentiate sphere volume V = (4/3)*pi*R^3 with respect to R!

1 Radius increases by dR = R * alpha * Delta T.

2 Volume of sphere: V = (4/3) * pi * R^3.

3 Differentiate: dV = (4/3) * pi * (3 * R^2 * dR) = 4 * pi * R^2 * dR.

4 Substitute dR: dV = 4 * pi * R^2 * (R * alpha * Delta T) = 4 * pi * R^3 * alpha * Delta T.

5 Notice: The factor 3 cancels cleanly! Instant answer in 10 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Volume expansion coefficient gamma = 3*alpha for isotropic materials. Fractional volume change is Delta V / V = gamma*Delta T = 3*alpha*Delta T. Multiplying by V = (4/3)*pi*R^3 yields Delta V = (4/3)*pi*R^3 * (3*alpha*Delta T) = 4*pi*R^3*alpha*Delta T.

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

State the Initial Volume and Volume Expansion Coefficient

For an isotropic metallic sphere of initial radius R:

V = \frac{4}{3} \pi R^3, \qquad \gamma = 3\alpha

• gamma is the coefficient of cubical (volume) expansion, which equals 3 times the linear coefficient alpha.

Step 2

Formulate the Change in Volume

The increase in volume for a small temperature rise Delta T is given by thermal expansion theory:

\Delta V = V \cdot \gamma \cdot \Delta T = V \cdot (3\alpha) \cdot \Delta T

• Valid for small temperature increments (Delta T << 1/alpha).

Step 3

Substitute Initial Volume and Simplify

Substitute V = (4/3) * pi * R^3 into the expansion formula:

\Delta V = \left( \frac{4}{3} \pi R^3 \right) \times (3\alpha \Delta T) = 4\pi R^3 \alpha \Delta T

• The factor of 3 in the numerator cancels the factor of 3 in the denominator.
• Leaves the exact result: 4 * pi * R^3 * alpha * Delta T.
• Matches Option (3) exactly.

⭐

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 Option (1)

✗ Incorrect

Verdict & Scientific Reason:

Uses areal expansion coefficient beta = 2*alpha.

⚠️

Student Fallacy (Why candidates pick this trap): Confuses volume expansion with surface area expansion (using factor 2 instead of 3).

Note: Volume expansion uses gamma = 3*alpha, not 2*alpha.

2 Option (2)

✗ Incorrect

Verdict & Scientific Reason:

Arithmetic factor error.

⚠️

Student Fallacy (Why candidates pick this trap): Drops the factor 4 from (4/3)*pi*R^3.

Note: Sphere volume has a factor of 4: (4/3)*pi*R^3.

3 Option (3)

✓ 100% Correct

Verdict & Scientific Reason:

100% mathematically exact; confirmed by Official NTA Final Answer Key.

💡

Why this is airtight: Flawless execution of gamma = 3*alpha and volume formula.

Note: Exact thermal physics.

4 Option (4)

✗ Incorrect

Verdict & Scientific Reason:

Spurious factor of 6.

⚠️

Student Fallacy (Why candidates pick this trap): Multiplies by 2 again or uses diameter instead of radius.

Note: Factor is exactly 4.

⚠️

NTA Trap Alert: Forgetting gamma = 3*alpha

Students who use Delta V = V * alpha * Delta T calculate (4/3)*pi*R^3*alpha*Delta T and get confused because it is not in the options.

🛡️ How to avoid the -1 mark: Always remember: Linear = alpha; Superficial/Area = 2*alpha; Cubical/Volume = 3*alpha!

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Core NEET Syllabus Standard

NEET UG Physics Core Standards · Thermal Properties of Matter Standard Benchmark

Core Scientific Principle Tested:

"For an isotropic solid, gamma = 3*alpha. Fractional volume change is dV/V = 3*alpha*dT."

Syllabus Focus: Thermal Expansion of Solids (Linear, Area, and Volume)

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2026 Physics Question 24 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Differential Volume Expansion Rule

Step-by-Step Rigorous Workflow & Mathematical Proof

State the Initial Volume and Volume Expansion Coefficient

Formulate the Change in Volume

Substitute Initial Volume and Simplify

360° Option Elimination Engine Key Feature

NTA Trap Alert: Forgetting gamma = 3*alpha

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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