Well the equation you need to use is:
(change in length)/(initial length) = (linear thermal expansion coefficient)*(change in temperature)

These are the expansion coeffiecients:
Brass 18.7*10^-6
Aluminum 22.2*10^-6

So for part a we need to find a change in T so the the diameters are equal. (the length in the equation is the diameter in this problem)

so for the brass ring:
x / 0.1 m = 18.7*10^-6 * (change in T)
for the aluminum rod
(x - .0001 m)/ 0.1001m = 22.2*10^-6 * (change in T)

Solving these equations my answer was:
x = -0.0005309 m or -0.053 cm
change in T = -283.9 C

So at a temperature of -263.9 C both diameters will be 9.947 cm,
which is attainable because absolute zero is -273.15 C

I'm not entirely sure this is right but I hope it helps.
Also I don't have time to work out b right now . but I might get to it tonight.
Source(s):
http://www.engineeringtoolbox.com/linear-expansion-coefficients-d_95.html
http://en.wikipedia.org/wiki/Coefficient_of_thermal_expansion


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