How Does Temperature Affect the Fit Between a Brass Ring and an Aluminum Rod?

[whitehorsey]

1.A brass ring of diameter 10.00 cm at 20.0°C is heated and slipped over an aluminum rod of diameter 10.01 cm at 20.0°C. Assuming the average coefficients of linear expansion are constant, (a) to what temperature must this combination be cooled to separate them? Is this attainable? (b) What if the aluminum rod were 10.02 cm in diameter?
L_frod = L_fring


2. Linear expansion of solids Δl = l₀αΔT



3. Shouldn't the temperature be heated instead to separate the ring and the rod because then it would expand? Also why is L_frod = L_fring?

 

[mfb]

If you heat the combined metals, both expand - what is the thermal expansion of aluminium, compared to the expansion of brass? Does heating (both together) work then?

What does L_frod = L_fring mean?
To find the point where they get separable, both should have the same diameter.