A) \[{{V}^{2}}\propto \lambda {{q}^{-1}}{{p}^{-1}}\]
B) \[{{V}^{2}}\propto g\lambda \]
C) \[{{V}^{2}}\propto \lambda gp\]
D) \[{{V}^{2}}\propto {{g}^{-1}}{{\lambda }^{-1}}\]
Correct Answer: B
Solution :
\[[L{{T}^{-1}}]={{[L]}^{X}}\,{{[M{{L}^{-3}}]}^{Y}}\,{{[L{{T}^{-2}}]}^{Z}}\] \[=[{{L}^{(X-3Y)+Z}}{{M}^{Y}}{{T}^{-32}}]\] Solving, we get, \[X=\frac{1}{2},\] \[Y=0\] and \[Z=\frac{1}{2}\] \[V\propto \sqrt{g\lambda }\] \[\Rightarrow \] \[{{V}^{2}}=g\lambda \]
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