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The only possible dimensionless group that combines velocity $V_1$ body size $L$,fluid density $\rho$ and surface tension coefficient $\sigma$ is

$\begin{array}{1 1}(A)\;\large\frac{L\rho \sigma}{V}\\(B)\;\large\frac{\rho V L^2}{\sigma}\\(C)\;\large\frac{\sigma L V^2}{\rho}\\(D)\;\large\frac{\rho LV^2}{\sigma}\end{array} $

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The dimensions of the physical quantity are $V=\large\frac{L}{t},$$L=L,\rho=\large\frac{m}{L^3}$ and $\sigma=\large\frac{m}{t^2}$
Put in option (d) & get it is dimensionless.
Hence (D) is the correct answer.
answered May 9, 2014 by sreemathi.v
 

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