91Ó°ÊÓ

step 1 is missing in the document.

The change in length of the metal rods is given by,

$∆L=∆L_A+∆L_B$

Here, $∆L_A$is the change in length of rod A and $∆L_B$is the change in the length of B.

The value of $∆L_A$is given by,

$∆L_A={\mathrm{Î\pm }}_A{L}_A∆T$

Here, ${\mathrm{Î\pm }}_A$is the coefficient of expansion, $L_A$is the length of rod A and $∆T$is the change in temperature.

Similarly,

$∆L_B={\mathrm{Î\pm }}_B{L}_B∆T$

Here, ${\mathrm{Î\pm }}_B$is the coefficient of expansion, $L_B$is the length of rod B and $∆T$is the change in temperature.

the length equation the value of $L_A$and $L_B$is given by,

$L_A=\frac{∆L/∆T-\left(-0.300\right){\mathrm{Î\pm }}_B}{{\mathrm{Î\pm }}_A-{\mathrm{Î\pm }}_B}$

And

$L_B=30cm-L_A$

Substitute all the values in the above two equations.

$$\begin{gathered} L_A=\frac{\left(0.058×{10}^{-2}m\right)/\left(100°C\right)-\left(0.300m\right)\left(1.65×{10}^{-5}{\left(°C\right)}^{-1}\right)}{1.00×{10}^{-5}{\left(°C\right)}^{-1}} \\ =23.0cm \\ {L}_B=30cm-23cm \\ =7cm \end{gathered}$$

Thus, the length of each portion A and B of rod is 23.0 cm and 7 cm respectively.