A) \[\sqrt{\frac{h{{c}^{5}}}{G}}\]
B) \[\sqrt{\frac{{{c}^{3}}}{Gh}}\]
C) \[\sqrt{\frac{Gh}{{{c}^{5}}}}\]
D) \[\sqrt{\frac{Gh}{{{c}^{3}}}}\]
Correct Answer: C
Solution :
| \[t={{G}^{a}}{{h}^{b}}{{C}^{c}}\] |
| \[\Rightarrow \] \[{{M}^{o}}{{L}^{o}}T'={{({{M}^{-\,1}}{{L}^{3}}{{T}^{-2}})}^{a}}{{(M{{L}^{2}}{{T}^{-\,1}})}^{b}}{{(L{{T}^{-\,1}})}^{c}}\] |
| \[\Rightarrow \] \[-a+b=0\]\[\Rightarrow \] \[a=b\] |
| \[\Rightarrow \] \[3a+2b+c=0\] |
| \[\Rightarrow \] \[c=-\,5a\] |
| \[\Rightarrow \] \[-\,2a-b-c=1\] |
| \[\Rightarrow \] \[a=\frac{1}{2};\]\[b=\frac{1}{2};\] \[c=-\frac{5}{2}\] |
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