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 {{\varepsilon }_{0}}}\times \frac{{{q}_{1}}{{q}_{2}}}{{{r}^{2}}} $ or $ {{\varepsilon }_{0}}=\frac{1\times {{q}_{1}}{{q}_{2}}}{F\times 4\pi {{r}^{2}}} $ Dimensions of $ [{{\varepsilon }_{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{align} & \because \,V=\frac{W}{Q} \\ & Q=IT \\ \end{align} \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}}] $