A) \[[M{{L}^{2}}{{T}^{-2}}]\]
B) \[[{{M}^{3/2}}{{L}^{3/2}}{{T}^{-2}}]\]
C) \[[M{{L}^{7/2}}{{T}^{-2}}]\]
D) \[[M{{L}^{3/2}}{{T}^{-2}}]\]
Correct Answer: C
Solution :
Given\[,E=\frac{P\sqrt{h}}{h+Q}\] ... (i) Dimension of \[E=\] Dimension of potential energy \[=[M{{L}^{2}}{{T}^{-2}}]\] From Eq. (i), we get Dimension of \[Q=\] Dimension of\[h=[{{M}^{0}}L{{T}^{0}}]\] \[\therefore \]Dimension of\[P\] \[=\frac{Dimension\,\,of\,\,E\times Dimension\,\,of\,\,(h+O)}{Dimension\,\,of\,\,\sqrt{h}}\] \[=\frac{[M{{L}^{2}}{{T}^{-2}}][{{M}^{0}}L{{T}^{0}}]}{[{{M}^{0}}{{L}^{1/2}}{{T}^{0}}]}=[M{{L}^{5/2}}{{T}^{-2}}]\] Hence, dimensions of\[PQ\] \[=[M{{L}^{5/2}}{{T}^{-2}}][{{M}^{0}}L{{T}^{0}}]=[M{{L}^{7/2}}{{T}^{-2}}]\]
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