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The torque $\backslash ($ T$\_\{$o$\}\backslash )$ of an electrically driven buffer used to wax and polish cars depends on the force of the buffer on the car surface $\backslash ($ F$\_\{$o$\}\backslash ),$ the rotational speed $\backslash (\backslash$omega $\backslash ),$ the height of the roughness elements on the car surface $\backslash ($ e $\backslash ),$ the viscosity of the wax or polishing fluid $\backslash (\backslash$mu $\backslash ),$ and the surface tension of the wax or polishing fluid $\backslash (\backslash$sigma $\backslash ).$ Use the force of the buffer, the rotational speed of the buffer, and the height of the roughness elements as repeating variables and develop a suitable set of pi terms for this problem. The first dimensionless group should contain the torque, the second dimensionless group should contain the viscosity and the third dimensionless group should contain the surface tension.

$\backslash [$

$\backslash$begin$\{$aligned$\}$

$\backslash$Pi$\_\{1\}$ & $=\backslash \backslash$

$\backslash$Pi$\_\{2\}$ & $=\backslash \backslash$

$\backslash$Pi$\_\{3\}$ & $=$

$\backslash$end$\{$aligned$\}$

$\backslash ]$

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$5\backslash \%$ score reduction after attempt $4$