In SI units, the dimensions of √((ε₀)/(μ₀)) is: (a) A–1 TML3 (b) A2T3M–1L–2 (c) AT–3ML3/2 (d) AT2M–1L–1

Answer: (b). [ε₀] = [M⁻¹L⁻³T⁴A²], [μ₀] = [MLT⁻²A⁻²] (ε₀)/(μ₀) = [M⁻²L⁻⁴T⁶A⁴] √((ε₀)/(μ₀)) = [M⁻¹L⁻²T³A²] (inverse of resistance) So the answer is (b) A²T³M⁻¹L⁻².

In SI units, the dimensions of √((ε₀)/(μ₀)) is: | JEE Main 2019 (8 Apr, Shift 1)

Q75JEE Main 2019 · 8 APR · SHIFT 1Easy

Units & Dimensions

In SI units, the dimensions of $\sqrt{\frac{\epsilon_0}{\mu_0}}$ is:

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Answer: (b)

$[\varepsilon_0] = [\mathrm{M^{-1}L^{-3}T^{4}A^{2}}]$ , $[\mu_0] = [\mathrm{MLT^{-2}A^{-2}}]$
$\frac{\varepsilon_0}{\mu_0} = [\mathrm{M^{-2}L^{-4}T^{6}A^{4}}]$
$\sqrt{\frac{\varepsilon_0}{\mu_0}} = [\mathrm{M^{-1}L^{-2}T^{3}A^{2}}]$ (inverse of resistance)
So the answer is (b) $\mathrm{A^2T^3M^{-1}L^{-2}}$ .

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Units & Dimensions question from JEE Main 2019 (8 Apr, Shift 1)

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