A solid circular high density polyethylene bar is to be forced to fit tightly inside a metal tube by the application of a load F$,$ shown. The tube has a diameter of $13\mathrm{.}8$ mm $,$ while the internal diameter of the solid bar is $13\mathrm{.}75$ mm $.$

If the properties of the solid bar are such that E is $1\mathrm{.}15$ GPa and $\backslash ($ v $\backslash )$ is $0\mathrm{.}39,$ determine, presenting ALL answers to $3$ significant figures.

$($i$)$ the axial$/$ longitudinal strain developed in the bar

$[3$ MARKS$]$

$($ii$)$ the force $($in kN $)$ required to ensure that the bar fits tightly within the hollow tube adopting the normal convention for the expression of the nature of the force applied.

$[3$ MARKS$]$

$($iii$)$ In your script books, for a further $6$ marks, draw the Mohr's Circle identifying the direct, principle and maximum shear stresses that may act on the element shown, when subjected to the applied force system. Plot your circle in N$/$mm$^2.$