Units & Dimensions

JEE Main level, single correct, medium

6 of 149

Question 6 of 149

Match List - I with List - II.
 List - I  List - II  (A)  Permeability of free space  (I) [M L2 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) [L2 A]\begin{array}{llll} & \text { List - I } & & \text { List - 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}

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

(A) B=μ0i2πr&qvB=FB=\frac{\mu_0 i}{2 \pi r} \& q v B=F
μ0≡Bri≡Frqvi≡MLT−2×L A2TLT−1≡MLT−2A−2\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≡FqV≡MLT−2ATLT−1=MT−2 A−1B \equiv \frac{F}{q V} \equiv \frac{\mathrm{MLT}^{-2}}{\mathrm{ATLT}^{-1}}=\mathrm{MT}^{-2} \mathrm{~A}^{-1}
(C) M=iA≡AL2M=i A \equiv \mathrm{AL}^2
(D) τ=Cθ⇒C≡ML2 T−2\tau=C \theta \Rightarrow C \equiv \mathrm{ML}^2 \mathrm{~T}^{-2}

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