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NEET
Exam
NEET
Subject
Physics
Chapter
Units and Dimensions

NEET · Physics · Units and Dimensions

Match List I with List II -I amp; -II A. amp; Torque amp; I. amp;...

Match List I with List II <tableclass="qx−match−listqx−match−table"border="1"cellpadding="6"cellspacing="0"><tr><td>\textList−I<table class="qx-match-list qx-match-table" border="1" cellpadding="6" cellspacing="0"><tr><td>\textList-Iamp; \textList-IIA.amp; Torqueamp; I.amp; {[M1L1T−2A−2]\left[M^1 L^1 T^{-2} A^{-2}\right]}B.amp; Magnetic fieldamp; II.amp; {[L2A1]\left[L^2 A^1\right]}C.amp; Magnetic momentamp; III.amp; {[M1T−2A−1]\left[M^1 T^{-2} A^{-1}\right]}D.amp; Permeability of free spaceamp; IV.amp; {[M1L2T−2]\left[M^1 L^2 T^{-2}\right]} Choose the correct answer from the options given below:

Options

  1. AA-III, B-I, C-II, D-IV
  2. BA-IV, B-II, C-III, D-I
  3. CA-IV, B-III, C-II, D-I
  4. DA-I, B-III, C-II, D-IV

Correct answer

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

Step-by-step solution

[τ⃗]=[r→×F→]=[ML2 T−2][F]=[qVB]⇒B=(FqV)=[MLT−2ATLT−1]=[MA−1 T−2][M]=[I×A]=[AL2]B=μ04πIdlsin⁡θr2⇒[μ]=[Br2Idl]=[MT−2 A−1×L2AL]=[MLT−2 A−2]\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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