Final answer:
The question asks for the ratio of the length of an aluminum rod to the total length of it combined with a steel rod when both rods expand equally due to temperature change. This involves using the linear thermal expansion formula and setting the expansions equal because the change in temperature is the same for both rods.
Step-by-step explanation:
The student's question involves finding the ratio of the length of an aluminum rod to the total length of two rods - one made of aluminum and the other made of steel - when the expansion in both rods is the same upon a change in temperature. The formula to use in this scenario is the linear thermal expansion formula, which is AL = αLΔT, where AL is the change in length, α is the coefficient of linear expansion, L is the original length of the rod, and ΔT is the change in temperature.
Given that the expansion of both rods is the same, we can set up the equation αaL1ΔT = αsL2ΔT. The change in temperature (ΔT) cancels out, leaving us with the ratio αa/αs = L2/L1. To find L1/(L1+L2), we rearrange this equation to solve for L1 in terms of L2 and then divide by the total length (L1+L2).