A) \[he_{{}}^{-2}\mu _{{}}^{-1}G_{{}}^{0}\]
B) \[h_{{}}^{2}eG_{{}}^{0}\mu \]
C) \[h_{{}}^{0}e_{{}}^{2}G_{{}}^{-1}\mu \]
D) \[hGe_{{}}^{-2}\mu _{{}}^{0}\]
Correct Answer: A
Solution :
[a] Here \[v={{e}^{a}}{{h}^{b}}{{\mu }^{c}}{{G}^{d}}\]. Taking the dimensions, \[{{M}^{0}}L{{T}^{-1}}{{A}^{0}}={{[A{{T}^{1}}]}^{a}}{{[M{{L}^{2}}{{T}^{-1}}]}^{b}}{{[ML{{T}^{-2}}{{A}^{-2}}]}^{c}}[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]\]There will be four simultaneous equations by equating the dimensions of M, L, T, and A. These are a-2c=0, a-b-2c solving for a, b, c, and d, we get a=-2, b=1, c=-1, d=0 Thus, \[v={{e}^{-2}}h{{\mu }^{-1}}{{G}^{0}}\]
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