A) \[{{S}^{3/2}}{{I}^{1/2}}{{h}^{0}}\]
B) \[{{S}^{1/2}}{{I}^{1/2}}{{h}^{0}}\]
C) \[{{S}^{1/2}}{{I}^{1/2}}{{h}^{-1}}\]
D) \[{{S}^{1/2}}{{I}^{3/2}}{{h}^{-1}}\]
Correct Answer: B
Solution :
\[p=k\,{{s}^{s}}{{I}^{b}}{{h}^{c}}\] where k is dimensionless constant \[ML{{T}^{-1}}={{(M{{T}^{-2}})}^{a}}{{(M{{L}^{2}})}^{b}}{{(M{{L}^{2}}{{T}^{-1}})}^{c}}\] \[a+b+c=1\] \[2b+2c=1\] \[2ac=1\] \[a=\frac{1}{2}\,\,\,\,\,\,\,\,\,\,\,b=\frac{1}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,c=0\] \[{{s}^{1/2}}{{I}^{1/2}}{{h}^{0}}\]
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