MCQ
Match List $I$ with List $II$

List $I$ List $II$
$A$ Torque  $I$ ${\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]}$
$B$ Magnetic fileld  $II$ $\left[\mathrm{L}^2 \mathrm{~A}^1\right]$
$C$ Magneti moment $III$ ${\left[\mathrm{M}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]}$
$D$ permeability of free  space $IV$ $\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]$

Choose the correct answer from the options given below :

  • A
    $A-I, B-III, C-II, D-IV$
  • $A-IV, B-III, C-II, D-I$
  • C
     $A-III, B-I, C-II, D-IV$
  • D
    $A-IV, B-II, C-III, D-I$

Answer

Correct option: B.
$A-IV, B-III, C-II, D-I$
b
${[\tilde{\tau}]=[\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}]=\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]}$

${[\mathrm{F}]=[\mathrm{qVB}]}$

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

${[\mathrm{M}]=[\mathrm{I} \times \mathrm{A}]=\left[\mathrm{AL}^2\right]}$

$\mathrm{B}=\frac{\mu_0}{4 \pi} \frac{\mathrm{Idl} \sin \theta}{\mathrm{r}^2}$

$\Rightarrow[\mu]=\left[\frac{\mathrm{Br}^2}{\mathrm{Idl}}\right]=\left[\frac{\mathrm{MT}^{-2} \mathrm{~A}^{-1} \times \mathrm{L}^2}{\mathrm{AL}}\right]$

$=\left[\mathrm{MLT}^{-2} \mathrm{~A}^{-2}\right]$

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