Match List I with List II List I List II (A) Permeability of free space I. [] (B) Magnetic field II. [] (C) Magnetic moment III. [] (D) Torsional constant IV. [] Choose the correct answer from the options given below : [2025]

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Q.
Match List I with List II

List I List II

(A) Permeability of free space I. [ $M L^{2} T^{- 2}$ ]

(B) Magnetic field II. [ $M T^{- 2} A^{- 1}$ ]

(C) Magnetic moment III. [ $M L T^{- 2} A^{- 2}$ ]

(D) Torsional constant IV. [ $L^{2} A$ ]

Choose the correct answer from the options given below : [2025]

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

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

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

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

Ans.
(4)

$B = \frac{μ_{0} I}{2 π r}$

$\Rightarrow [μ_{0}] = [\frac{B \cdot r}{I}] = [\frac{M T^{- 2} A^{- 1} \times L}{A}] = [M L T^{- 2} A^{- 2}]$

magnetic field F = qvB

$B = [\frac{M L T^{- 2}}{A T L / T}] = [M T^{- 2} A^{- 1}]$

$[M] = [L^{2} A]$

$τ = C θ \Rightarrow C = [\frac{τ}{θ}] = [M L^{2} T^{- 2}]$

Solution

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

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

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

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

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	List I		List II
(A)	Permeability of free space	I.	[ $M L^{2} T^{- 2}$ ]
(B)	Magnetic field	II.	[ $M T^{- 2} A^{- 1}$ ]
(C)	Magnetic moment	III.	[ $M L T^{- 2} A^{- 2}$ ]
(D)	Torsional constant	IV.	[ $L^{2} A$ ]

Solution

Q. Match List I with List II List I List II (A) Permeability of free space I. [ML2T–2] (B) Magnetic field II. [MT–2A–1] (C) Magnetic moment III. [MLT–2A–2] (D) Torsional constant IV. [L2A] Choose the correct answer from the options given below : [2025]

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

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

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

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

Ans. (4) B=μ0I2πr ⇒ [μ0]=[B·rI]=[MT–2A–1×LA]=[MLT–2A–2] magnetic field F = qvB B=[MLT–2ATL/T]=[MT–2A–1] [M]=[L2A] τ=Cθ ⇒ C=[τθ]=[ML2T–2]

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