In Order to Make a Tight Fit Between Two Metal $\circ$

In order to make a tight fit between two metal parts,machinists sometimes make the interior part larger than the hole into which it will fit,and then either cool the interior part or heat the exterior piece so that the pieces will fit.Consider fitting an aluminum rod with diameter D₁ (at 25 ^$\circ$ C) into a D₂ = 12.000 mm (at 25 ^$\circ$ C) diameter hole in a brass plate.The machinists can cool the rod to 77 K by immersing it in liquid nitrogen.What is the largest possible diameter D₁ of the rod at 25 ^$\circ$ C that will just fit into the hole if the rod has been cooled to 77 K and the brass plate has been left at 25 ^$\circ$ C? The coefficients of thermal expansion for aluminum and brass are 22 * 10^-6 K^-1 and 19*10^-6 K^-1,respectively.

A) 11.941 mm
B) 12.000 mm
C) 12.014 mm
D) 12.032 mm
E) 12.058 mm

Correct Answer:

Verified

Unlock this answer now
Get Access to more Verified Answers free of charge

Access For Free