Question

Match the LIST-I with LIST-II 

Choose the correct answer from the options given below:

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

Hint:

Always derive dimensions using defining equations rather than memorizing them.

Answer 1

The Correct Option is A

To solve this problem, we need to match each physical quantity in List-I with its corresponding dimensional formula in List-II: 

List-I	List-II
A. Spring constant	I. \( ML^2T^{-2}K^{-1} \)
B. Thermal conductivity	II. \( M L^0 T^{-2} \)
C. Boltzmann constant	III. \( M L^2 T^{-3} A^{-2} \)
D. Inductive reactance	IV. \( ML T^{-3}K^{-1} \)

1. Spring Constant (A): The dimensional formula for spring constant \( k \) is \( [MLT^{-2}] \). It aligns with option II \( M L^0 T^{-2} \).
2. Thermal Conductivity (B): The dimensional formula for thermal conductivity \( k \) is \( [MLT^{-3} \theta^{-1}] \). It aligns with option IV \( ML T^{-3} K^{-1} \).
3. Boltzmann Constant (C): The dimensional formula for Boltzmann constant is \( [ML^2T^{-2}K^{-1}] \). It aligns with option I \( ML^2 T^{-2} K^{-1} \).
4. Inductive Reactance (D): The dimensional formula for inductive reactance is \( [ML^2T^{-3}A^{-2}] \). It aligns with option III \( M L^2 T^{-3} A^{-2} \).

Therefore, the correct matching is:

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

This matches the correct answer option provided. Each correspondence was verified using the standard dimensional formulas associated with each quantity.