What is the density in (mg/L) of a copper wire with a density of 8920 kg/m^3 and a radius of .1mm? Assume the wire is infinite in length.
You wish to calculate the density of a copper wire in units of mg/L (miligrams per litre) when the density is in units of kg/m^3 (kilograms per metre cubed).
The density of a wire does not depend upon either the length of the wire nor the radius. All that matters is that `10^6mg=1kg` and that `1L=(10cmxx10cmxx10cm)=10^-3m^3`.
From this, it can be worked out that:
and from here:
When converting from one unit to another, the value is multiplied by the conversion factor for the numerators of the units (in this case, kg to mg) and divided by the conversion factor for the denominator of the units (in this case, `m^3` to L). This is fully explained in the reference below.