In SI units, the dimensions of $\sqrt{\frac{\epsilon_{0}}{\mu_{0}}}$ is:

(C) $\mathrm{A}^{2} \mathrm{~T}^{3} \mathrm{M}^{-1} \mathrm{~L}^{-2}$

(A) $\mathrm{AT}^{-3} \mathrm{ML}^{3 / 2}$

(B) $\mathrm{A}^{-1} \mathrm{TML}{ }^{3}$

(D) $\mathrm{AT}^{2} \mathrm{M}^{-1} \mathrm{~L}^{-1}$

JEE Main · 2019 · 08 Apr 2019 · Shift 1 · Units & Measurement

In SI units, the dimensions of

\frac{ϵ _{0}}{μ _{0}}

is:

Answer: (C)

Write out the base dimensions:

ϵ_{0}

M^{- 1} L^{- 3} T^{4} A^{2}

and

μ_{0}

M L T^{- 2} A^{- 2}

. Their ratio is

\frac{ϵ _{0}}{μ _{0}} = M^{- 2} L^{- 4} T^{6} A^{4}

, and taking the square root halves every exponent to give

M^{- 1} L^{- 2} T^{3} A^{2}

, which is the dimensional formula of

ϵ_{0} / μ_{0}

JEE Main · 2019 · 08 Apr 2019 · Shift 1 · Single correct option