Match List - I with List - II. array llll & - I & & - 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) &

Correct answer: B. (A)-(III), (B)-(II), (C)-(IV), (D)-(I) (A) B=(μ_0 i)/(2 π r) \& q v B=F μ_0 (B r)/(i) (F r)/(q v i) MLT^ -2 × L ~A^2 TLT^ -1 MLT^ -2 A^ -2 (B) B (F)/(q V) MLT^ -2 ATLT^ -1 =MT^ -2 ~A^ -1 (C) M=i A AL^2 (D) =C θ C ML^2 ~T^ -2

JEE Main 202523 JanuaryEvening Shift

Exam: JEE Main
Year: 2025
Date: 23 January
Shift: Evening Shift
Subject: Physics
Chapter: Units and Dimensions

JEE Main 2025 · 23 January · Evening Shift · Physics · Units and Dimensions

Match List - I with List - II. array llll & - I & & - II (A) &...

Match List - I with List - II.

\begin{array}{llll} & \textList - I & & \textList - II \\ \text{ (A) } & \text{ Permeability of free space } & \text{ (I) }\left[\mathrm{M} \mathrm{ L}^2 \mathrm{ T}^{-2}\right] \\ \text{ (B) } & \text{ Magnetic field } & \text{ (II) }\left[\mathrm{M} \mathrm{ T}^{-2} \mathrm{ A}^{-1}\right] \\ \text{ (C) } & \text{ Magnetic moment } & \text{ (III) }\left[\mathrm{M} \mathrm{ L} \mathrm{ T}^{-2} \mathrm{ A}^{-2}\right] \\ \text{ (D) } & \text{ Torsional constant } & \text{ (IV) }\left[\mathrm{L}^2 \mathrm{ A}\right] \end{array}

Choose the correct answer from the options given below :

Options

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

Correct answer

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

Step-by-step solution

(A)

B=\frac{\mu_0 i}{2 \pi r} \& q v B=F

\mu_0 \equiv \frac{B r}{i} \equiv \frac{F r}{q v i} \equiv \frac{\mathrm{MLT}^{-2} \times L}{\mathrm{~A}^2 \mathrm{TLT}^{-1}} \equiv \mathrm{MLT}^{-2} A^{-2}

(B)

B \equiv \frac{F}{q V} \equiv \frac{\mathrm{MLT}^{-2}}{\mathrm{ATLT}^{-1}}=\mathrm{MT}^{-2} \mathrm{~A}^{-1}

(C)

M=i A \equiv \mathrm{AL}^2

(D)

\tau=C \theta \Rightarrow C \equiv \mathrm{ML}^2 \mathrm{~T}^{-2}

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