Match List I with List II LIST I LIST 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 answer from the options given below :

Physics · Units, Dimensions & Error Analysis

JEE Main 2024 — 6 April, Shift 1 — Question 41

Match List I with List II

	LIST I		LIST II
A.	Torque	I.	$\left[ {{\text{M}}^{1}}\text{ }\!\!~\!\!\text{ }{{\text{L}}^{1}}\text{ }\!\!~\!\!\text{ }{{\text{T}}^{-2}}\text{ }\!\!~\!\!\text{ }{{\text{A}}^{-2}} \right]$
B.	Magnetic field	II.	$\left[ {{\text{L}}^{2}}\text{ }\!\!~\!\!\text{ }{{\text{A}}^{1}} \right]$
C.	Magnetic moment	III.	$\left[ {{\text{M}}^{1}}\text{ }\!\!~\!\!\text{ }{{\text{T}}^{-2}}\text{ }\!\!~\!\!\text{ }{{\text{A}}^{-1}} \right]$
D.	Permeability of free space	IV.	$\left[ {{\text{M}}^{1}}\text{ }\!\!~\!\!\text{ }{{\text{L}}^{2}}\text{ }\!\!~\!\!\text{ }{{\text{T}}^{-2}} \right]$

Choose the correct answer from the options given below :

Option A:
A-I, B-III, C-II, D-IV
Option B:
A-IV, B-III, C-II, D-I
Correct
Option C:
A-III, B-I, C-II, D-IV
Option D:
A-IV, B-II, C-III, D-I

Answer: B

Step-by-step solution

$[\vec{\tau}]=[\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}]=\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]$

$[\mathrm{F}]=[\mathrm{qVB}]$ $\Rightarrow \mathrm{B}=\left(\frac{\mathrm{F}}{\mathrm{qV}}\right)=\left[\frac{\mathrm{MLT}^{-2}}{\mathrm{ATLT}^{-1}}\right]=\left[\mathrm{MA}^{-1} \mathrm{~T}^{-2}\right]$ $[\mathrm{M}]=[\mathrm{I} \times \mathrm{A}]=\left[\mathrm{AL}^{2}\right]$

$B=\frac{\mu_{0}}{4 \pi} \frac{\mathrm{Idl} \sin \theta}{\mathrm{r}^{2}}$ $\begin{aligned} \Rightarrow[\mu]=\left[\frac{\mathrm{Br}^{2}}{\mathrm{Idl}}\right] & =\left[\frac{\mathrm{MT}^{-2} \mathrm{~A}^{-1} \times \mathrm{L}^{2}}{\mathrm{AL}}\right] & =\left[\mathrm{MLT}^{-2} \mathrm{~A}^{-2}\right]\end{aligned}$

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Exam: JEE Main 2024
Paper: 6 April, Shift 1
Subject: Physics
Chapter: Units, Dimensions & Error Analysis
Topic: Units and Dimensions Analysis

Answer: B

Step-by-step solution

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