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I have written a paper on the effect of change in mass on the drag coefficient of a ping pong ball. While making my last calculations, I decided to use the slope of the final graph (where the $x$ axis is the mass condition and the $y$ axis is the drag coefficient) to do error calculations. When I turned my paper in, my teacher asked for me to declare the unit for the slopes' of the maximum and minimum worst lines of best fit.

My problem is that I don't really know what the unit would be as drag coefficient is dimensionless. I have thought about using an arbitrary unit, but any help would be appreciated.

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  • $\begingroup$ I don't think there is any unit of drag coefficient. $\endgroup$
    – Vansh Patel
    Commented Nov 17 at 13:06
  • $\begingroup$ So is it fine if I use an arbitrary unit for the slope of the graph? $\endgroup$
    – Bubber-ducky
    Commented Nov 17 at 13:10
  • $\begingroup$ I think instead of using an arbitrary unit, $\text{kg}^{-1}$ or $\text{g}^{-1}$ would be more preferable $\endgroup$
    – Vansh Patel
    Commented Nov 17 at 13:13
  • $\begingroup$ Thanks a lot for your help. Do you think kg^-1 fine or should I go for Cd kg^-1? $\endgroup$
    – Bubber-ducky
    Commented Nov 17 at 13:26
  • $\begingroup$ I think $\text{kg}^{-1}$ would be fine. $\endgroup$
    – Vansh Patel
    Commented Nov 17 at 13:47

1 Answer 1

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By definition, the slope of a graph is the ratio between the vertical variation (drag coefficient) and the horizontal variation (mass). If you want the unit for the slope, it will therefore be $\text{kg}^{-1}$ if mass is measured in kilograms.

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