A bar $ABC$ of length $L$ consists of two parts of equal lengths but different diameters. Segment $AB$ has diameter $d_1 = 100$ mm, and segment $BC$ has diameter $d_2 = 60$ mm. Both segments have length $\frac{L}{2} = 1$ m. A longitudinal hole of diameter $d$ is drilled through segment $AB$ for one-half of its length (distance $\frac{L}{4} = 0.5$ m). The bar is made of plastic having modulus of elasticity $E = 7.0$ GPa. Compressive loads $P = 115$ kN act at the ends of the bar.
(a) If the shortening of the bar is limited to 8.0 mm, what is the maximum allowable diameter $d_{max}$ of the hole? Round your answer to one decimal place.
$d_{max} = \boxed{\phantom{00.0}}$ mm
(b) Now, if $d_{max}$ is instead set at $\frac{d_2}{2}$, at what distance $b$ from end $C$ should load $P$ be applied to limit the bar shortening to 8.0 mm? Round your answer to one decimal place.
$b = \boxed{\phantom{00.0}}$ mm
(c) Finally, if loads $P$ are applied at the ends and $d_{max} = \frac{d_2}{2}$, what is the permissible length $x$ of the hole if shortening is to be limited to 8.0 mm? Round your answer to one decimal place.
$x = \boxed{\phantom{00.0}}$ mm
