JEE Main 2025 Jan 23 Shift 2, Physics Q9: Units And Dimensions

JEE Main2025Jan 23, Shift 2Physics

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 :

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)

Solution

Derive each dimension from a defining relation.

(A) $μ_{0}$ : from $B = \frac{μ _{0} I}{2 π r}$ , $[μ_{0}] = \frac{[ B ] [ r ]}{[ I ]} = \frac{( M T ^{- 2} A ^{- 1} ) ( L )}{A} = [M L T^{- 2} A^{- 2}]$ . $\to$ (III)

(B) $B$ : from $F = q v B$ , $[B] = \frac{[ F ]}{[ q v ]} = \frac{M L T ^{- 2}}{( A T ) ( L T ^{- 1} )} = [M T^{- 2} A^{- 1}]$ . $\to$ (II)

(C) Magnetic moment $m$ : from $m = N I A$ , $[m] = (A) (L^{2}) = [L^{2} A]$ . $\to$ (IV)

(D) Torsional constant $c$ : from $τ = c θ$ with $θ$ dimensionless, $[c] = [τ] = [M L^{2} T^{- 2}]$ . $\to$ (I)

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

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JEE Main 2025 Jan 23 Shift 2, Physics Q9: Units And Dimensions

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