Question

Match List-I with List-II

where \[ \text{(I)}\ [ML^2T^{-3}A^{-1}] \] \[ \text{(II)}\ [M^0L^2A] \] \[ \text{(III)}\ [ML^2T^{-2}A^{-1}] \] \[ \text{(IV)}\ [ML^2T^{-2}A^{-2}] \] Choose the correct answer from the options given below:

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

Hint:

Important dimensions: \[ \text{EMF}=[ML^2T^{-3}A^{-1}] \] \[ \text{Magnetic Flux}=[ML^2T^{-2}A^{-1}] \] \[ \text{Inductance}=[ML^2T^{-2}A^{-2}] \] \[ \text{Magnetic Moment}=[L^2A] \] These are frequently asked in matching-type questions.

Answer 1

The Correct Option is A

Step 1:Dimension of Mutual Inductance. Using \[ L=\frac{\Phi}{I} \] \[ [L] = \frac{ML^2T^{-2}A^{-1}}{A} \] \[ [L] = ML^2T^{-2}A^{-2} \] Hence, \[ (A)\rightarrow(IV) \]

Step 2: Dimension of Magnetic Flux. \[ \Phi = BA \] Since \[ [B]=MT^{-2}A^{-1} \] \[ [\Phi] = ML^2T^{-2}A^{-1} \] Hence, \[ (B)\rightarrow(III) \]

Step 3: Dimension of EMF. \[ \text{EMF} = \frac{\text{Work}}{\text{Charge}} \] \[ [V] = \frac{ML^2T^{-2}}{AT} \] \[ [V] = ML^2T^{-3}A^{-1} \] Hence, \[ (C)\rightarrow(I) \]

Step 4: Dimension of Magnetic Moment. \[ M = IA \] \[ [M] = A\times L^2 \] \[ [M] = M^0L^2A \] Hence, \[ (D)\rightarrow(II) \]

Step 5: Write the final matching. \[ (A)\rightarrow(IV) \] \[ (B)\rightarrow(III) \] \[ (C)\rightarrow(I) \] \[ (D)\rightarrow(II) \] \[ { (A)-(IV),\ (B)-(III),\ (C)-(I),\ (D)-(II) } \] Hence, the correct option is \[ {(A)} \]