Q.37 Physics ⭐ 360° Option Elimination Active

NEET 2026 Physics Question 37 Solution

Topic: Units & Dimensions · Official NTA Booklet Code 50

Question

Consider that σₛ, k_B, b represent Stefan-Boltzmann constant, Boltzmann constant and Wien's displacement law constant, respectively. The dimension of σₛ k_B⁻¹ b is:

✓

Verified Against NTA Final Answer Key

Option (1) : [L^-1 T^-1 K^-2]

📚 Units & Dimensions Medium

📋 Given Parameters & Problem Setup

Stefan-Boltzmann Constant sigma_s

Boltzmann Constant k_B

Wien's Displacement Law Constant b

Target Product Dimension of sigma_s * k_B^-1 * b

⚡

The 30-Second Exam Hall Shortcut: ⚡ SI Units Product Method

⏱️ Saves 60 seconds of matrix-style dimensional algebra.

Work in base SI units: Watts, Joules, Meters, Kelvins!

1 sigma_s unit: W / (m^2 * K^4) = J / (s * m^2 * K^4).

2 k_B^-1 unit: (J / K)^-1 = K / J.

3 b unit: m * K.

4 Multiply units: [J / (s * m^2 * K^4)] * [K / J] * [m * K] = [J cancels!] / [s * m * K^2].

5 Remaining base units: m^-1 * s^-1 * K^-2.

6 In dimensions: [L^-1 T^-1 K^-2]. Solved in 20 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Writing units directly cancels Joules immediately, avoiding lengthy MLT substitutions and preventing algebraic exponent sign errors.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Determine Dimensions of Stefan-Boltzmann Constant sigma_s

From Stefan's law for radiant energy emitted per unit area per second:

E = \sigma_s T^4 \implies \sigma_s = \frac{\text{Power}}{\text{Area} \cdot T^4} = \frac{\text{M} \text{L}^2 \text{T}^{-3}}{\text{L}^2 \cdot \text{K}^4} = [\text{M} \text{T}^{-3} \text{K}^{-4}]

• Radiant energy per second is Power: [M L^2 T^-3].
• Dividing by area [L^2] and temperature to the fourth [K^4] gives [M T^-3 K^-4].

Step 2

Determine Dimensions of Boltzmann Constant k_B and Wien Constant b

From kinetic theory of gases and Wien's displacement law:

[k_B] = \frac{[\text{Energy}]}{[T]} = [\text{M} \text{L}^2 \text{T}^{-2} \text{K}^{-1}] \implies [k_B^{-1}] = [\text{M}^{-1} \text{L}^{-2} \text{T}^2 \text{K}^1]

• Wien's law: lambda_{max} * T = b ==> [b] = [L K].

Step 3

Multiply and Simplify the Dimensional Expression

Combine all three dimensional terms:

[\sigma_s k_B^{-1} b] = [\text{M} \text{T}^{-3} \text{K}^{-4}] \times [\text{M}^{-1} \text{L}^{-2} \text{T}^2 \text{K}^1] \times [\text{L} \text{K}]

• Mass: M^{1 - 1} = M^0 (mass cancels completely).
• Length: L^{-2 + 1} = L^{-1}.
• Time: T^{-3 + 2} = T^{-1}.
• Temperature: K^{-4 + 1 + 1} = K^{-2}.
• Final combined dimension: [L^-1 T^-1 K^-2].
• Matches Option (1) 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)

✓ 100% Correct

Verdict & Scientific Reason:

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

💡

Why this is airtight: Correctly simplifies powers of M, L, T, and K.

Note: Exact dimensional physics.

2 Option (2)

✗ Incorrect

Verdict & Scientific Reason:

Missing time dimension T^-1.

⚠️

Student Fallacy (Why candidates pick this trap): Assumes Stefan's constant is energy per area rather than power per area, dropping T^-1.

Note: Stefan's law involves energy rate (watts), which has time T^-1.

3 Option (3)

✗ Incorrect

Verdict & Scientific Reason:

Temperature exponent arithmetic error.

⚠️

Student Fallacy (Why candidates pick this trap): Computes -4 + 1 = -3 and forgets the factor of K from Wien's constant b.

Note: b has dimension [L K], contributing an additional +1 to the temperature power.

4 Option (4)

✗ Incorrect

Verdict & Scientific Reason:

Ignores both temperature offsets.

⚠️

Student Fallacy (Why candidates pick this trap): Leaves K^-4 from Stefan's constant unchanged.

Note: Both k_B^-1 (+1) and b (+1) modify the temperature exponent.

⚠️

NTA Trap Alert: Dropping the Wien Temperature Factor [K]

Students frequently remember Wien's law as lambda = b/T and mistakenly take [b] = [L / K] instead of [b] = [L * K], leading to Option (3).

🛡️ How to avoid the -1 mark: Remember the product: lambda_max * T = b. Length * Temperature = Meter * Kelvin = [L K].

📖

Core NEET Syllabus Standard

NEET UG Physics Core Standards · Units and Measurements Standard Benchmark

Core Scientific Principle Tested:

"Dimensional consistency: Multiply component dimensions algebraically. In radiation: [sigma_s] = M T^-3 K^-4, [k_B] = M L^2 T^-2 K^-1, and [b] = L K."

Syllabus Focus: Dimensional Analysis and Physical Constants of Thermal Radiation

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2026 Physics Question 37 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ SI Units Product Method

Step-by-Step Rigorous Workflow & Mathematical Proof

Determine Dimensions of Stefan-Boltzmann Constant sigma_s

Determine Dimensions of Boltzmann Constant k_B and Wien Constant b

Multiply and Simplify the Dimensional Expression

360° Option Elimination Engine Key Feature

NTA Trap Alert: Dropping the Wien Temperature Factor [K]

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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