Match List - I with List - II. List - I A. Boltzmann constant B. Stefan's constant C. Planck's constant D. Gravitational constant List - II I. [M-1 L3 T-2] II. [M L2 T-1] III. [M L2 T-2 K-1] IV. [M L0 T-3 K-4] Choose the correct answer from the options given below :

The correct answer is Option 3. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Physics Q27 – JEE-MAIN 2026

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Match List - I with List - II.

\begin{array}{lcl} List - I & List - II \\ A. Boltzmann constant & I. [M^{- 1} L^{3} T^{- 2}] \\ B. Stefan's constant & II. [M L^{2} T^{- 1}] \\ C. Planck's constant & III. [M L^{2} T^{- 2} K^{- 1}] \\ D. Gravitational constant & IV. [M L^{0} T^{- 3} K^{- 4}] \end{array}

Choose the correct answer from the options given below :

Clue 1 of 3: Dimensional Analysis

Recall the fundamental definitions and formulas for each physical constant to determine their dimensions.

🧠 Full Solution Path

Step 1: Determine dimensions of Boltzmann constant (

k_{B}

) and Stefan's constant (

σ

).✦ Active

For Boltzmann constant ( $k_{B}$ ): From the relation $E = k_{B} T$ , we have $k_{B} = E / T$ . The dimensions of energy $E$ are $[M L^{2} T^{- 2}]$ and temperature $T$ are $[K]$ . Therefore, the dimensions of $k_{B}$ are $[M L^{2} T^{- 2} K^{- 1}]$ . This matches List-II, III.

For Stefan's constant ( $σ$ ): From Stefan-Boltzmann law, power radiated per unit area is $P / A = σ T^{4}$ . So, $σ = P / (A T^{4})$ . The dimensions of power $P$ are $[M L^{2} T^{- 3}]$ , area $A$ are $[L^{2}]$ , and temperature $T$ are $[K]$ . Therefore, the dimensions of $σ$ are $[M L^{2} T^{- 3}] / ([L^{2}] [K^{4}]) = [M L^{0} T^{- 3} K^{- 4}]$ . This matches List-II, IV.

Step 2: Determine dimensions of Planck's constant (

h

) and Gravitational constant (

G

).○ Expand

For Planck's constant ( $h$ ): From the relation $E = h ν$ , we have $h = E / ν$ . The dimensions of energy $E$ are $[M L^{2} T^{- 2}]$ and frequency $ν$ are $[T^{- 1}]$ . Therefore, the dimensions of $h$ are $[M L^{2} T^{- 2}] / [T^{- 1}] = [M L^{2} T^{- 1}]$ . This matches List-II, II.

For Gravitational constant ( $G$ ): From Newton's law of gravitation, $F = G \frac{m_{1} m_{2}}{r^{2}}$ . So, $G = \frac{F r^{2}}{m_{1} m_{2}}$ . The dimensions of force $F$ are $[M L T^{- 2}]$ , distance $r$ are $[L]$ , and mass $m$ are $[M]$ . Therefore, the dimensions of $G$ are $\frac{[M L T^{- 2}] [L^{2}]}{[M^{2}]} = [M^{- 1} L^{3} T^{- 2}]$ . This matches List-II, I.

Step 3: Match the constants to their dimensions and select the correct option.○ Expand

Based on the derivations:

A. Boltzmann constant $\to$ III. $[M L^{2} T^{- 2} K^{- 1}]$

B. Stefan's constant $\to$ IV. $[M L^{0} T^{- 3} K^{- 4}]$

C. Planck's constant $\to$ II. $[M L^{2} T^{- 1}]$

D. Gravitational constant $\to$ I. $[M^{- 1} L^{3} T^{- 2}]$

This combination corresponds to option "3".

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Physics Question 27 – JEE-MAIN 2026

Clue 1 of 3: Dimensional Analysis

🧠 Full Solution Path