Answer
9.996 cm
Work Step by Step
The coefficient of linear expansion $\alpha$ of the given aluminum-alloy rod is not readily available to us. We should find that.
We know that $\Delta L=L\alpha\Delta T$
$\implies \alpha=\frac{\Delta L}{L\Delta T}=\frac{(10.015-10.000)cm}{10.000\,cm\times(100-20)^{\circ}C}=1.875\times10^{-5}/C^{\circ}$
Let $L_{new}$ be the length of the rod at the freezing point of water, Then
$L_{new}=L+\Delta L=L+L\alpha\Delta T=L(1+\alpha\Delta T)$
$=10.000\,cm(1+1.875\times10^{-5}/C^{\circ}\times(0-20.000)^{\circ}C)=9.996\,cm$
