Answer
The glass rod must be heated to a temperature of $116.7^{\circ}C$
Work Step by Step
We can find an expression for the increase in length of the lead rod when it is heated:
$\Delta L = \alpha~\Delta T~L$
$\Delta L = (29\times 10^{-6}~K^{-1})(30.0~K)~L$
$\Delta L = 870~L~\times 10^{-6}$
We can find the required change in temperature of the glass rod so that the increases in length of the two rods are equal:
$\Delta L = \alpha~\Delta T~L$
$870~L~\times 10^{-6} = (9\times 10^{-6}~K^{-1})~\Delta T~L$
$\Delta T = \frac{870~L~\times 10^{-6}}{9~L\times 10^{-6}}$
$\Delta T = 96.7~K$
$\Delta T = 96.7^{\circ}C$
Since the initial temperature was $20.0^{\circ}C$, the glass rod must be heated to a temperature of $116.7^{\circ}C$.
