$($b$)$ A rotameter calibrated for metering has a scale ranging from $0\mathrm{.}014\frac{m^3}{m}in$ to $0\mathrm{.}14\frac{m^3}{m}in.$ It is intended to use this meter for metering a gas of density $1\mathrm{.}3k\frac{g}{m^3}$ with in a flow range of $0\mathrm{.}028\frac{m^3}{m}in$ to $0\mathrm{.}28\frac{m^3}{m}in.$ What should be the density of the new float if the original one has a density of $1900k\frac{g}{m^3}?$ Both the floats can be assumed to have the same volume and shape.

$[6]$