Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): It is impossible for two rods made of different materials and having identical initial lengths to maintain a constant difference in length when subjected to the same temperature change. Reason (R): The difference in length of two rods remains independent of temperature only if their initial lengths

Step-by-step solution

For the difference in length of two rods to remain independent of temperature, their individual changes in length must be equal: L₁ = L₂ L₁ ₁ T = L₂ ₂ T L₁ ₁ = L₂ ₂ L₁ L₂ = ₂ 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 ( ₁ ₂ ). For the product L to be equal for both rods, their initial lengths cannot be identical ( L₁ L₂ )