In terms of resistance R and time T , the dimensions of ratio (μ)/( ) of the permeability μ and permittivity is:

Correct answer: C. [R^2] Dimensions of μ= [. MLT .^ -2 A^ -2 ] Dimensions of ∈= [M^ -1 L^ -3 T^4 A^2] Dimensions of R= [ML^2 T^ -3 A^ -2 ] aligned & Dimensions of μ Dimensions of e = [MLT^ -2 A^ -2 ] [M^ -1 L^ -3 T^4 A^2] &=[M^2 L^4 T^ -6 A^ -4 ]=[R^2] aligned

JEE Main 201411 AprilOnline

Exam: JEE Main
Year: 2014
Date: 11 April
Mode: Online
Subject: Physics
Chapter: Units and Dimensions

JEE Main 2014 · 11 April · Online · Physics · Units and Dimensions

In terms of resistance R and time T , the dimensions of ratio (μ)/(...

In terms of resistance

R

and time

T

, the dimensions of ratio

\frac{\mu}{\varepsilon}

of the permeability

\mu

and permittivity

\varepsilon

is:

Options

A $\left[\mathrm{RT}^{-2}\right]$
B $\left[\mathrm{R}^2 \mathrm{~T}^{-1}\right]$
C $\left[\mathrm{R}^2\right]$
D $\left[\mathrm{R}^2 \mathrm{~T}^2\right]$

Correct answer

C. $\left[\mathrm{R}^2\right]$

Step-by-step solution

Dimensions of

\mu= \left[\right. MLT \left.^{-2} \mathrm{ A}^{-2}\right] Dimensions

\in= \left[\mathrm{M}^{-1} \mathrm{ L}^{-3} \mathrm{ T}^4 \mathrm{ A}^2\right]

Dimensions of

\mathrm{R}= \left[\mathrm{ML}^2 \mathrm{ T}^{-3} \mathrm{ A}^{-2}\right]

\begin{aligned}&\therefore \frac{\text{ Dimensions\text{ of } } \mu}{\text{ Dimensions of } e}=\frac{\left[\mathrm{MLT}^{-2} \mathrm{ A}^{-2}\right]}{\left[\mathrm{M}^{-1} \mathrm{ L}^{-3} \mathrm{ T}^4 \mathrm{ A}^2\right]}\\ &=\left[\mathrm{M}^2 \mathrm{ L}^4 \mathrm{ T}^{-6} \mathrm{ A}^{-4}\right]=\left[\mathrm{R}^2\right] \end{aligned}

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