A) \[[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\]
B) \[[{{M}^{1}}{{L}^{0}}{{T}^{0}}]\]
C) \[[{{M}^{0}}{{L}^{1}}{{T}^{0}}]\]
D) \[[{{M}^{0}}{{L}^{0}}{{T}^{1}}]\]
Correct Answer: A
Solution :
[a] \[[e]=[AT],{{L}_{0}}=[{{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{A}^{2}}]\]= \[[M{{L}^{2}}{{T}^{-1}}]\]and \[[c]=[L{{T}^{-1}}]\] \[\left[ \frac{{{e}^{2}}}{4\pi {{\in }_{0}}hc} \right]=\left[ \frac{{{A}^{2}}{{T}^{2}}}{{{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{A}^{2}}\times M{{L}^{2}}{{T}^{-1}}\times L{{T}^{-1}}} \right]\]\[=[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\]
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