A cyclone separator is operating in conditions where D$($cut$)=10$ um$.$ We are offered another cyclone that is of the same design, but all the dimensions are one$-$half as big as the present one. If we feed the same air stream $($same total volumetric flow rate, same particle loading, same particle size distribution$)$ to this new cyclone, what will the new value of D$($cut$)$ be$?$ Assume that Eq$.(9\mathrm{.}18)$ is applicable.