\(2.22 \times 10^{-5} \mathrm{k}^{-1}\)
given:
\begin{array}{l}
l_{\mathrm{c}}=30 \mathrm{~cm} \\
\Delta \theta=60^{\circ} \mathrm{C} \\
l_{\mathrm{f}}=30.04 \mathrm{~cm} \\
\alpha=?
\end{array}
using \( \alpha=\frac{\Delta l}{l_0 \Delta \theta}\)
\begin{array}{l}
\Delta l=l_f-l_0=30.04-30=0.04 \mathrm{~cm} \\
\alpha=\frac{0.04}{30 \times 60}=0.00002222 \\
\alpha=2.22 \times 10^{-5} \mathrm{k}^{-1}
\end{array}