Question

Match List-I with List-II.

Choose the correct answer.

• A. A-I, B-II, C-III, D-IV
• B. A-IV, B-III, C-II, D-I
• C. A-III, B-IV, C-II, D-I
• D. A-II, B-I, C-IV, D-III

Answer 1

The Correct Option is C

Concept: Dimensional formulas of important physical constants:

• Boltzmann constant \(k\): relates energy with temperature. \[ [E]=[ML^2T^{-2}] \] Thus \[ k=\frac{E}{T} \] \[ [ML^2T^{-2}K^{-1}] \]
• Stefan–Boltzmann constant \(\sigma\): from Stefan’s law \[ E=\sigma T^4 \] \[ \sigma=[ML^0T^{-3}K^{-4}] \]
• Planck's constant \(h\): \[ E=h\nu \] \[ h=\frac{E}{\nu} \] \[ [ML^2T^{-1}] \]
• Gravitational constant \(G\): From Newton’s law \[ F=\frac{Gm_1m_2}{r^2} \] Thus \[ G=[M^{-1}L^3T^{-2}] \]

Step 1: {Match the constants.} \[ A \rightarrow III \] \[ B \rightarrow IV \] \[ C \rightarrow II \] \[ D \rightarrow I \] Hence the correct match is: \[ \text{A-III, B-IV, C-II, D-I} \]