A

Step 1: Calculate the change in length of each rod due to the temperature increase. The formula for the change in length (9;ΔL9;) due to linear expansion is given by:

$$ \Delta L = L \cdot \alpha \cdot \Delta T $$
For the first rod:
$$ \Delta L_1 = L_1 \cdot \alpha_1 \cdot T $$
For the second rod:
$$ \Delta L_2 = L_2 \cdot \alpha_2 \cdot T $$
Step 2: The final lengths of the rods after the temperature increase will be:
$$ L_{1f} = L_1 + \Delta L_1 = L_1 + L_1 \cdot \alpha_1 \cdot T $$
$$ L_{2f} = L_2 + \Delta L_2 = L_2 + L_2 \cdot \alpha_2 \cdot T $$
Step 3: Determine the effective lengths of the rods when they are constrained at both ends (the total extension should equal the available space):
Let the total extension be equal to the length of the system, with the walls remaining fixed. Thus, the rods must exert equal and opposite forces on each other, and we can use the formula for stress and strain to find the force:

$$ F = Y \cdot \frac{\Delta L}{L} \cdot A $$
Step 4: Substitute for the first and second rods:
The force on the first rod:
$$ F_1 = Y_1 \cdot \frac{\Delta L_1}{L_1} \cdot A = Y_1 \cdot \frac{L_1 \cdot \alpha_1 \cdot T}{L_1} \cdot A = Y_1 \cdot \alpha_1 \cdot T \cdot A $$
The force on the second rod:
$$ F_2 = Y_2 \cdot \frac{\Delta L_2}{L_2} \cdot A = Y_2 \cdot \frac{L_2 \cdot \alpha_2 \cdot T}{L_2} \cdot A = Y_2 \cdot \alpha_2 \cdot T \cdot A $$
Step 5: Setting the forces equal (since they act against each other):
$$ F_1 = F_2 \implies Y_1 \cdot \alpha_1 \, T = Y_2 \cdot \alpha_2 \, T $$
Thus, simplifying gives:9;
$$ \frac{Y_1 \cdot \alpha_1}{Y_2 \cdot \alpha_2} = 1 $$
The resultant force exerted by the expanded rods on each other is given by:
$$ F = Y \cdot \frac{\Delta L}{L} \cdot A $$
Thus, the final answer can be represented as:
Force with which the rods act on each other:
$$ F = \frac{Y_1 \cdot \alpha_1 T + Y_2 \cdot \alpha_2 T}{2} A $$
Therefore, A.