Q 12-02-132JEE MainJEE Main 2021 (27 Jul, Shift 2)Easy
Match List-I with List-II.
**List-I**
(a) Capacitance, $C$
(b) Permittivity of free space, $\varepsilon_0$
(c) Permeability of free space, $\mu_0$
(d) Electric field, $E$
**List-II**
(i) $M^1L^1T^{-3}A^{-1}$
(ii) $M^{-1}L^{-3}T^4A^2$
(iii) $M^{-1}L^{-2}T^4A^2$
(iv) $M^1L^1T^{-2}A^{-2}$
Choose the correct answer from the options given below.
Answer: (A) (a)→(iii), (b)→(ii), (c)→(iv), (d)→(i)
$C = \dfrac{Q}{V} = \dfrac{AT}{ML^2T^{-3}A^{-1}} = M^{-1}L^{-2}T^4A^2$ → (iii)
$\varepsilon_0 = \dfrac{q^2}{4\pi Fr^2} = \dfrac{A^2T^2}{MLT^{-2}L^2} = M^{-1}L^{-3}T^4A^2$ → (ii)
$\mu_0 = \dfrac{1}{\varepsilon_0c^2} = MLT^{-2}A^{-2}$ → (iv)
$E = \dfrac Fq = \dfrac{MLT^{-2}}{AT} = MLT^{-3}A^{-1}$ → (i)
Solution by Sreeraj P, M.Sc Physics