Problem $3$:

A $12$ in $.$ long nylon $]$ rod $(1)$ having a diameter of $d=1\mathrm{.}6in.$ is placed inside a steel $E=29200$ksi;$v=0\mathrm{.}3$ tube $(2)$ as shown in the figure. The inside diameter of the steel tube is $D=1\mathrm{.}65$ in$.$ An external load $P$ is applied to the nylon rod, compressing it$.$

a$)$ At what value of $P$ will the space between the nylon rod and the steel tube be closed?