Question

Match List-I with List-II. 

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

Hint:

In dimensional analysis, match the physical quantities with their corresponding dimensions based on the units involved.

Answer 1

The Correct Option is D

To match the items from List-I with those in List-II, let's identify the dimensional formulas for each physical quantity. 

1. Permeability of free space (A): 
   The dimensional formula is \([M L T^{-2} A^{-2}]\).
   Thus, (A) matches with (III).
2. Magnetic field (B): 
   The dimensional formula is \([M T^{-2} A^{-1}]\).
   Thus, (B) matches with (II).
3. Magnetic moment (C): 
   The dimensional formula is \([L^2 A]\).
   Thus, (C) matches with (IV).
4. Torsional constant (D): 
   The dimensional formula is \([M L^2 T^{-2}]\).
   Thus, (D) matches with (I).

Hence, the correct matching is:

(A)-(III), (B)-(II), (C)-(IV), (D)-(I).

The correct answer is: (A)-(III), (B)-(II), (C)-(IV), (D)-(I)

Answer 2

Permeability of free space \( \mu_0 \) has the dimensional formula \( [M L^3 T^{-4} A^{-2}] \).
- Magnetic field \( B \) has the dimensional formula \( [M T^{-2} A^{-1}] \).
- Magnetic moment \( M \) has the dimensional formula \( [M L T^{-2} A^{-2}] \).
- Torsional constant has the dimensional formula \( [L^2 A] \). Thus, the correct matching is: \[ % Option (A)-(III), (B)-(II), (C)-(IV), (D)-(I). \]