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JEE Main 202127 JulyEvening Shift
Exam
JEE Main
Year
2021
Date
27 July
Shift
Evening Shift
Subject
Physics
Chapter
Units and Dimensions

JEE Main 2021 · 27 July · Evening Shift · Physics · Units and Dimensions

Match List I with List II. List-I List-II a Capacitance, C i M ^ 1...

Match List I with List II.

List-I List-II
a Capacitance, C i M1L1T−3A−1{M}^{1}{L}^{1}{T}^{- 3}{A}^{- 1}
b Permittivity of free space, ε0{ε}_{0} ii M−1L−3T4A2{M}^{- 1}{L}^{- 3}{T}^{4}{A}^{2}
c Permeability of free space, μ0{\mu}_{0} iii M−1L−2T4A2{M}^{- 1}{L}^{- 2}{T}^{4}{A}^{2}
d Electric field, E iv M1L1T−2A−2{M}^{1}{L}^{1}{T}^{- 2}{A}^{- 2}

Choose the correct answer from the options given below

Options

  1. A(a)→(iii),(b)→(ii),(c)→(iv),(d)→(i)( a ) \to ( iii ), ( b ) \to ( ii ) , ( c ) \to ( iv ) , ( d ) \to ( i )
  2. B(a)→(iii),(b)→(iv),(c)→(ii),(d)→(i)( a ) \to ( iii ), ( b ) \to ( iv ), ( c ) \to ( ii ), ( d ) \to ( i )
  3. C(a)→(iv),(b)→(ii),(c)→(iii),(d)→(i)( a ) \to ( iv ), ( b ) \to ( ii ), ( c ) \to ( iii ), ( d ) \to ( i )
  4. D(a)→(iv),(b)→(iii),(c)→(ii),(d)→(i)( a ) \to ( iv ), ( b ) \to ( iii ), ( c ) \to ( ii ), ( d ) \to ( i )

Correct answer

A. (a)→(iii),(b)→(ii),(c)→(iv),(d)→(i)( a ) \to ( iii ), ( b ) \to ( ii ) , ( c ) \to ( iv ) , ( d ) \to ( i )

Step-by-step solution

q=CVq = CV

[C]=[qV]=(A×T)2ML2T−2[ C ] = \left[\dfrac{q}{V}\right] = \dfrac{( A \times T{)}^{2}}{{ML}^{2}{T}^{- 2}}

=M−1L−2T4A2= {M}^{- 1}{L}^{- 2}{T}^{4}{A}^{2}

[E]=[Fq]=MLT−2AT[ E ] = \left[\dfrac{F}{q}\right] = \dfrac{{MLT}^{- 2}}{AT}

=MLT−3A−1= {MLT}^{- 3}{A}^{- 1}

F=q1q24π∈0r2F = \dfrac{{q}_{1}{q}_{2}}{4\pi{\in}_{0}{r}^{2}}

\left[{ϵ}_{o}\right] = {M}^{- 1}{L}^{- 3}{T}^{4}{A}^{2}</p><p>Speedoflight</p><p>Speed of lightc = \dfrac{1}{\sqrt{{\mu}_{0}{\in}_{o}}}</p><p></p><p>{\mu}_{0} = \dfrac{1}{{ϵ}_{0}{c}^{2}}</p><p>[μ0]=1[M−1L−3T4A2][LT−1]2</p><p>\left[{\mu}_{0}\right] = \dfrac{1}{\left[{M}^{- 1}{L}^{- 3}{T}^{4}{A}^{2}\right]{\left[{LT}^{- 1}\right]}^{2}}

=[M1L1T−2A−2]= \left[{M}^{1}{L}^{1}{T}^{- 2}{A}^{- 2}\right]

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