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Question

Match List-I with List-II:

| List-I | List-II |
|---|---|
| (A) Coefficient of viscosity | (I) $[ML^2T^{-2}]$ |
| (B) Surface tension | (II) $[ML^2T^{-1}]$ |
| (C) Angular momentum | (III) $[ML^{-1}T^{-1}]$ |
| (D) Rotational kinetic energy | (IV) $[ML^0T^{-2}]$ |

Choose the correct answer from the options given below: A). (A)-(II), (B)-(I), (C)-(IV), (D)-(III) B). (A)-(I), (B)-(II), (C)-(III), (D)-(IV) C). (A)-(III), (B)-(IV), (C)-(II), (D)-(I) D). (A)-(IV), (B)-(III), (C)-(II), (D)-(I)

Edvaya · Accepted Answer

The correct answer is (A)-(III), (B)-(IV), (C)-(II), (D)-(I). Finding the dimensional formula for each quantity:
**(A) Coefficient of viscosity:** $\eta = F/(A \cdot dv/dy) \Rightarrow [ML^{-1}T^{-1}]$ → **(III)**
**(B) Surface tension:** $T = F/l \Rightarrow [MT^{-2}] = [ML^0T^{-2}]$ → **(IV)**
**(C) Angular momentum:** $L = I\omega = [ML^2][T^{-1}] = [ML^2T^{-1}]$ → **(II)**
**(D) Rotational kinetic energy:** $KE = \frac{1}{2}I\omega^2 = [ML^2][T^{-2}] = [ML^2T^{-2}]$ → **(I)**
Correct match: A→(III), B→(IV), C→(II), D→(I).

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List-I	List-II
(A) Coefficient of viscosity	(I) $[ML^2T^{-2}]$
(B) Surface tension	(II) $[ML^2T^{-1}]$
(C) Angular momentum	(III) $[ML^{-1}T^{-1}]$
(D) Rotational kinetic energy	(IV) $[ML^0T^{-2}]$