Question

The correct order in which the dimension of Length increases in the following physical quantities is?

• A. A, B, C, D
• B. D, C, B, A
• C. A, D,
• D. C, B, C, A

Answer 1

Answer: (C)

For dimension of permittivity is given by $\because$ $F=\frac{1}{4\pi {\epsilon }_0}\times \frac{q_1{q}_2}{r^2}$ or ${\epsilon }_0=\frac{1\times q_1{q}_2}{F\times 4\pi r^2}$ Dimensions of $[{\epsilon }_0]=\frac{[IT\times IT]}{[ML{T}^{-2}][L^2]}$ $=[M^{-1}{L}^{-3}{T}^4{I}^2]$ For dimensions of resistance $\because$ $R=\frac{V}{I}=\frac{W}{QI}=\frac{W}{ITI}$ $\left(\begin{array}{rl}& \because V=\frac{W}{Q}\\ & Q=IT\end{array}\right)$ $=\frac{[M{L}^2{T}^{-2}]}{[I^{2}T]}=[M{L}^2{T}^{-3}{I}^{-2}]$ For dimensions of magnetic permeability $\because$ $F=\frac{{\mu }_0}{2\pi }\times \frac{I_1{I}_{1}l}{r}$ or ${\mu }_0=\frac{F\times 2\pi r}{I_1{I}_{2}l}$ Dimensions of $[{\mu }_0]=\frac{[ML{T}^{-2}][L]}{[I^2][L]}=[ML{T}^{-1}{I}^{-2}]$ For dimensions of stress $\because$ $Stress=\frac{force}{area}$ $=\frac{[ML{T}^{-2}]}{[L^2]}=[M{L}^{-1}{T}^{-2}]$