A steel ring with a $2\mathrm{.}5000$ in$.$ inside diameter at $20\mathrm{.}0$o C is to be warmed and slipped over a brass shaft with a $2\mathrm{.}5020$ in$.$ outside diameter at $20\mathrm{.}0$o C$.$

$($a$)$ To what temperature should the ring be warmed?

$($b$)$ If the ring and the shaft together are cooled by some means such as liquid air, at what temperature will the ring just slip off the shaft?