Match List I with List II -I -II A. Torque I. [M^1 L^1 T^ -2 A^ -2 ] B. Magnetic field II. [L^2 A^1] C. Magnetic moment III. [M^1 T^ -2 A^ -1 ] D. Permeability of free space IV. [M^1 L^2 T^ -2 ] Choose the correct

Correct answer: C. A-IV, B-III, C-II, D-I aligned & [ ]=[ r × F ]=[ML^2 ~T^ -2 ] & [F]=[qVB] & B=( F qV )=[ MLT^ -2 ATLT^ -1 ]=[MA^ -1 ~T^ -2 ] & [M]=[I × A]=[AL^2] & B=(μ_0)/(4 π) Idl θ r^2 & [μ]=[ Br^2 Idl ]=[ MT^ -2 ~A^ -1 × L^2 AL ] & =[MLT^ -2 ~A^ -2 ] aligned

JEE Main 20246 AprilMorning Shift

Exam: JEE Main
Year: 2024
Date: 6 April
Shift: Morning Shift
Subject: Physics
Chapter: Units and Dimensions

JEE Main 2024 · 6 April · Morning Shift · Physics · Units and Dimensions

Match List I with List II -I -II A. Torque I. [M^1 L^1 T^ -2 A^ -2...

Match List I with List II

<table class="qx-match-list qx-match-table" border="1" cellpadding="6" cellspacing="0"><tr><td>\textList-I

\textList-IIA.TorqueI.{\left[M^1 L^1 T^{-2} A^{-2}\right]

}</td></tr><tr><td>B.</td><td>Magnetic field</td><td>II.</td><td>{\left[L^2 A^1\right]

}C.Magnetic momentIII.{\left[M^1 T^{-2} A^{-1}\right]

}</td></tr><tr><td>D.</td><td>Permeability of free space</td><td>IV.</td><td>{\left[M^1 L^2 T^{-2}\right]

} Choose the correct answer from the options given below:

Options

AA-III, B-I, C-II, D-IV
BA-IV, B-II, C-III, D-I
CA-IV, B-III, C-II, D-I
DA-I, B-III, C-II, D-IV

Correct answer

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

Step-by-step solution

\begin{aligned} & {[\vec{\tau}]=[\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}]=\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]} \\ & {[\mathrm{F}]=[\mathrm{qVB}]} \\ & \Rightarrow \mathrm{B}=\left(\frac{\mathrm{F}}{\mathrm{qV}}\right)=\left[\frac{\mathrm{MLT}^{-2}}{\mathrm{ATLT}^{-1}}\right]=\left[\mathrm{MA}^{-1} \mathrm{~T}^{-2}\right] \\ & {[\mathrm{M}]=[\mathrm{I} \times \mathrm{A}]=\left[\mathrm{AL}^2\right]} \\ & \mathrm{B}=\frac{\mu_0}{4 \pi} \frac{\mathrm{Idl} \sin \theta}{\mathrm{r}^2} \\ & \Rightarrow[\mu]=\left[\frac{\mathrm{Br}^2}{\mathrm{Idl}}\right]=\left[\frac{\mathrm{MT}^{-2} \mathrm{~A}^{-1} \times \mathrm{L}^2}{\mathrm{AL}}\right] \\ & =\left[\mathrm{MLT}^{-2} \mathrm{~A}^{-2}\right]\end{aligned}

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