Match List I with List II. Choose the correct answer from the options given below List - I List - II (a) Capacitance, C (i) M¹L¹T⁻³A⁻¹ (b) Permittivity of free space, ε₀ (ii) M⁻¹L⁻³T⁴A² (c) Permeability of free space, μ₀ (iii) M⁻¹L⁻²T⁴A² (d) Electric field, E (iv) M¹L¹T⁻²A⁻² (a) (a) → (iii), (b) → (ii), (c) → (iv), (d) → (i) (b) (a) → (iii), (b) → (iv), (c) → (ii), (d) → (i) (c) (a) → (iv), (b) → (ii), (c) → (iii), (d) → (i) (d) (a) → (iv), (b) → (iii), (c) → (ii), (d) → (i)

Answer: (a). Capacitance C = q/V = [AT][ML²T⁻³A⁻¹] = [M⁻¹L⁻²T⁴A²] → (iii). ε₀ = (q²)/(4π F r²) = [M⁻¹L⁻³T⁴A²] → (ii). μ₀ = (1)/(ε₀ c²) = [MLT⁻²A⁻²] → (iv). E = F/q = [MLT⁻³A⁻¹] → (i). So the answer is (a) (a)-(iii), (b)-(ii), (c)-(iv), (d)-(i).

Match List I with List II. Choose the correct answer from the options… | JEE Main 2021 (27 Jul, Shift 2)

Q64JEE Main 2021 · 27 JUL · SHIFT 2Medium

Units & Dimensions

Match List I with List II.

Choose the correct answer from the options given below

	List - I		List - II
(a)	Capacitance, C	(i)	$M^{1}L^{1}T^{-3}A^{-1}$
(b)	Permittivity of free space, $\varepsilon_0$	(ii)	$M^{-1}L^{-3}T^{4}A^{2}$
(c)	Permeability of free space, $\mu_0$	(iii)	$M^{-1}L^{-2}T^{4}A^{2}$
(d)	Electric field, E	(iv)	$M^{1}L^{1}T^{-2}A^{-2}$

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Answer: (a)

Capacitance $C = \dfrac{q}{V} = \dfrac{[\mathrm{AT}]}{[\mathrm{ML^2T^{-3}A^{-1}}]} = [\mathrm{M^{-1}L^{-2}T^4A^2}]$ → (iii).
$\varepsilon_0 = \dfrac{q^2}{4\pi F r^2} = [\mathrm{M^{-1}L^{-3}T^4A^2}]$ → (ii).
$\mu_0 = \dfrac{1}{\varepsilon_0 c^2} = [\mathrm{MLT^{-2}A^{-2}}]$ → (iv).
$E = F/q = [\mathrm{MLT^{-3}A^{-1}}]$ → (i).
So the answer is (a) (a)-(iii), (b)-(ii), (c)-(iv), (d)-(i).

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