A) \[{{v}^{2}}\propto \lambda {{g}^{-1}}{{\rho }^{-1}}\]
B) \[{{v}^{2}}\propto \,g\lambda \rho \]
C) \[{{v}^{2}}\propto \,g\lambda \]
D) \[{{v}^{2}}\propto \,{{g}^{-1}}\lambda {{\rho }^{-3}}\]
Correct Answer: C
Solution :
[c] \[v\,\propto \,{{(\lambda )}^{a}}\,{{(\ell )}^{b}}{{(g)}^{c}}\] \[v\,\propto \,{{(L)}^{a}}\,{{(M{{L}^{-3}})}^{b}}{{(L{{T}^{-2}})}^{c}}\] \[v=k\,{{M}^{b}}\,{{L}^{a-3b+c}}{{T}^{-2c}}\] \[L{{T}^{-1}}=k\,{{M}^{b}}{{L}^{a-\,3b+c}}\,{{T}^{-2c}}\] \[a-3b+c=1,-2c=-1b=0\] \[a-3\times 0+\frac{1}{2}=1,\,\,\,c=\frac{1}{2}\] \[a=\frac{1}{2}\] \[v=k\,{{(\lambda )}^{{}^{1}/{}_{2}}}{{(\ell )}^{o}}\,{{(g)}^{{}^{1}/{}_{2}}}\] \[{{V}_{2}}=k(\lambda )(g)\]
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