A cylindrical assembly consisting of a brass core and an aluminum collar is compressed by a load P. The length of the aluminum collar and brass core is [tex]350 \mathrm{~mm}[/tex], the diameter of the core is [tex]25 \mathrm{~mm}[/tex], and the outside diameter of the collar is 40 [tex]\mathrm{mm}[/tex]. Also, the moduli of elasticity of the aluminum and brass are [tex]72 \mathrm{GPa}[/tex] and [tex]100 \mathrm{GPa}[/tex], respectively. (a) If the length of the assembly decreases by [tex]0.1 \%[/tex] when the load [tex]\mathrm{P}[/tex] is applied, what is the magnitude of the load? (b) What is the maximum permissible load [tex]P_{\max }[/tex] if the allowable stresses in the aluminum and brass are [tex]80 \mathrm{MPa}[/tex] and [tex]120 \mathrm{MPa}[/tex], respectively?
