$(10$ pts$)$ The change in diameter with temperature for a solid material can be expressed as follows:

$\frac{d_f-d_0}{d_0}={}_l(T_f-T_0)$

where ${}_l$ is the linear coefficient of thermal expansion.

To what temperature $($in degrees C$)$ must a cylindrical rod of metal A $10\mathrm{.}033$ mm in diameter and a plate of metal B having a circular hole $9\mathrm{.}984$ mm in diameter have to be heated for the rod to just fit into the hole?

Assume that the initial temperature is $22C$ and that the linear expansion coefficient values for metals A and $B$ are $4\mathrm{.}4{10}^{-6}(C{)}^{-1}$ and $16{10}^{-6}(C{)}^{-1},$ respectively