Two rods of equal length 60 cm each are joined together end to end. Coefficient of linear expansions of the rods are \( 24 \times 10^{-6} \, \text{°C}^{-1} \) and \( 1.2 \times 10^{-5} \, \text{°C}^{-1} \). Their temperatures are the same and equal to \( 30^\circ \text{C} \), which is increased to \( 100^\circ \text{C} \). Find final length of the combination (in cm).
Show Hint
When combining rods with different coefficients of linear expansion, calculate the individual length changes and sum them to get the total change in length.
Step 1: Formula for linear expansion.
The linear expansion of each rod is given by \( \Delta L = L \alpha \Delta T \). The total change in length is the sum of the changes in length of each rod. Step 2: Calculate the change in length.
For rod 1:
\[
\Delta L_1 = 60 \times (3.6 \times 10^{-5} \times 70) = 0.1512 \, \text{cm}
\]
For rod 2:
\[
\Delta L_2 = 60 \times (1.2 \times 10^{-5} \times 70) = 0.1512 \, \text{cm}
\]
Thus, the total change in length is \( 0.1512 \, \text{cm} \). The final length of the combination is:
\[
L_f = 120 + 0.1512 = 120.1512 \, \text{cm}
\]
Step 3: Conclusion.
The final length of the combination is \( 120.1512 \, \text{cm} \), which corresponds to option (3).
