A) \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }\]
B) \[[M{{L}^{-1}}{{T}^{-2}}]\]
C) \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{-2}}}{{\text{T}}^{\text{-1}}}\text{ }\!\!]\!\!\text{ }\]
D) \[\text{ }\!\![\!\!\text{ ML}{{\text{T}}^{\text{-1}}}\text{ }\!\!]\!\!\text{ }\]
Correct Answer: B
Solution :
Dimensions of \[{{\varepsilon }_{0}}=[{{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{A}^{2}}]\] Dimensions of\[E=[ML{{T}^{-3}}{{A}^{-1}}]\] \[\therefore \]Dimensions of\[\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}=[{{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{A}^{2}}]\] \[\times [{{M}^{2}}{{L}^{2}}{{T}^{-6}}{{A}^{-2}}]\] \[=[M{{L}^{-1}}{{T}^{-3}}]\]
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