A) \[{{A}^{-1}}TM{{L}^{3}}\]
B) \[{{A}^{2}}{{T}^{3}}{{M}^{-1}}{{L}^{-2}}\]
C) \[A{{T}^{2}}{{M}^{-1}}{{L}^{-1}}\]
D) \[A{{T}^{-3}}M{{L}^{3/2}}\]
Correct Answer: B
Solution :
| [b] dimension of\[\sqrt{\frac{{{\varepsilon }_{0}}}{{{\mu }_{0}}}}\] |
| \[[{{\varepsilon }_{0}}]=[{{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{A}^{2}}]\] |
| \[[{{\mu }_{0}}]=[ML{{T}^{-2}}{{A}^{-2}}]\] |
| dimensions of\[\sqrt{\frac{{{\varepsilon }_{0}}}{{{\mu }_{0}}}}={{\left[ \frac{{{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{A}^{2}}}{ML{{T}^{-2}}{{A}^{-2}}} \right]}^{\frac{1}{2}}}\] |
| \[={{[{{M}^{-2}}{{L}^{-4}}{{T}^{6}}{{A}^{4}}]}^{1/2}}\] |
| \[=[{{M}^{-1}}{{L}^{-2}}{{T}^{3}}{{A}^{2}}]\] |
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