Given below are two statements: one is labelled as Assertion (A)...

For the difference in length of two rods to remain independent of temperature, their individual changes in length must be equal:
$\Delta L_1 = \Delta L_2$

$L_1 \alpha_1 \Delta T = L_2 \alpha_2 \Delta T$

$L_1 \alpha_1 = L_2 \alpha_2$

$\dfrac{L_1}{L_2} = \dfrac{\alpha_2}{\alpha_1}$

This shows that the initial lengths must be inversely proportional to their coefficients of linear expansion. Thus, Reason (R) is true.

If the two rods are made of different materials, they have different coefficients of linear expansion ($\alpha_1 \neq \alpha_2$). For the product $L \alpha$ to be equal for both rods, their initial lengths cannot be identical ($L_1 \neq L_2$). Therefore, two different materials with identical initial lengths cannot maintain a constant difference in length. Thus, Assertion (A) is true.

Since Reason (R) provides the exact mathematical condition that proves Assertion (A), it is the correct explanation.

Answer: Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).