Question

Match List - I with List - II.

Choose the correct answer from the options given below:

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

Hint:

Understanding dimensional analysis is crucial for matching physical quantities correctly.

Answer 1

The Correct Option is D

• Angular Impulse = \( M L^2 T^{-1} \)
• Latent Heat = \( M^0 L^2 T^{-2} \)
• Electrical Resistivity = \( M L^3 T^{-3} A^{-2} \)
• Electromotive Force = \( M L^2 T^{-3} A^{-1} \)

Answer 2

Step 1: Understanding the question.
We are given two lists — List I contains physical quantities, and List II contains their corresponding dimensional formulas. We need to correctly match each quantity with its respective dimensional formula.

List - I	List - II
(A) Angular Impulse	(IV) \( ML^2T^{-1} \)
(B) Latent Heat	(I) \( M^0L^2T^{-2} \)
(C) Electrical Resistivity	(III) \( ML^3T^{-3}A^{-2} \)
(D) Electromotive Force (EMF)	(II) \( ML^2T^{-3}A^{-1} \)

Final Matching:
(A)-(IV), (B)-(I), (C)-(III), (D)-(II) Step 2: Recall the dimensional formulas.
- (A) Angular Impulse:
Angular Impulse = Change in Angular Momentum.
Dimensional formula of Angular Momentum = \( ML^2T^{-1} \).
Hence, Angular Impulse → \( ML^2T^{-1} \) → (IV).

- (B) Latent Heat:
Latent Heat = Energy / Mass.
Energy has the dimension \( ML^2T^{-2} \), so Latent Heat → \( M^0L^2T^{-2} \) → (I).

- (C) Electrical Resistivity:
Resistivity = Resistance × (Area / Length).
Resistance \( R = \frac{V}{I} \) and \( V = Work / Charge = (ML^2T^{-2}) / (AT) = ML^2T^{-3}A^{-1} \).
Thus, Resistance → \( ML^2T^{-3}A^{-2} \).
Multiplying by Area/Length → \( L^3T^{-3}A^{-2} \).
Hence, Resistivity → \( ML^3T^{-3}A^{-2} \) → (III).

- (D) Electromotive Force (EMF):
EMF is the potential difference; its dimensional formula is the same as that of voltage → \( ML^2T^{-3}A^{-1} \) → (II).

Step 3: Correct matching.
(A) Angular Impulse → (IV) \( ML^2T^{-1} \)
(B) Latent Heat → (I) \( M^0L^2T^{-2} \)
(C) Electrical Resistivity → (III) \( ML^3T^{-3}A^{-2} \)
(D) Electromotive Force → (II) \( ML^2T^{-3}A^{-1} \)

Final Answer:
\[ \boxed{(A)-(IV), (B)-(I), (C)-(III), (D)-(II)} \]