A) \[\frac{\rho {{\sigma }^{2}}}{{{p}^{3}}}\]
B) \[\frac{\rho {{\sigma }^{3}}}{\sigma }\]
C) \[\frac{{{\rho }^{3}}\sigma }{\rho }\]
D) \[\frac{\rho }{{{p}^{3}}\sigma }\]
Correct Answer: A
Solution :
Here, \[{{T}^{2}}={{p}^{a}}{{\rho }^{b}}{{\sigma }^{c}}\] ?.(i) Putting the dimensions of R.H.S. quantities, we get \[={{[M{{L}^{-1}}{{T}^{-2}}]}^{a}}{{[M{{L}^{-3}}]}^{b}}{{[M{{T}^{-2}}]}^{c}}\] \[=[{{M}^{a+b+c}}{{L}^{-a-3b}}{{T}^{-2a-2c}}]\] Hence, \[a+b+c=0\] \[-a-3b=0\] and \[-2a-2c=2\] On solving, we get \[a=-3,\text{ }b=1\]and\[c=2\] So, after putting the values of a, b and c in Eq. (i), we get \[{{T}^{2}}=\frac{\rho {{\sigma }^{2}}}{{{p}^{3}}}\]
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