A) \[\left[ {{M}^{0}}{{L}^{0}}{{T}^{0}} \right]\]
B) \[\left[ {{M}^{0}}L{{T}^{0}} \right]\]
C) \[\left[ {{M}^{0}}{{L}^{2}}{{T}^{-2}} \right]\]
D) \[\left[ {{M}^{0}}{{L}^{2}}{{T}^{-4}} \right]\]
Correct Answer: C
Solution :
According to Bernoullis theorem\[\frac{P}{d}+\frac{{{V}^{2}}}{2}+gh=cons\tan t\] Since, only same quantities can be added or subtracted. Therefore, dimensional formula of the constant = Dimensional formula of\[\frac{P}{d}\] = Dimensional formula of \[{{V}^{2}}/2\] = Dimensional formula of gh \[\because \] Dimensional formula of \[g=[{{M}^{0}}{{L}^{1}}{{T}^{-2}}]\] Dimensional formula of\[h=[{{M}^{0}}{{L}^{1}}{{T}^{0}}]\] \[\because \] Dimensional formula of the constant \[=[{{M}^{0}}{{L}^{1}}{{T}^{-2}}][{{M}^{0}}{{L}^{1}}{{T}^{0}}]=[{{M}^{0}}{{L}^{2}}{{T}^{-2}}]\]
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