A plate made of steel has a 18.9979 mm diameter hole cut into it. A 19.0000 mm diameter ball made of glass is sitting in the hole. Both are at an initial temperature of 9.00 deg. C. If the plate and ball are both heated, at what temperature will the ball just fit through the hole? (Steel coefficient = 12x10^-6 and glass coefficient = 9 x 10^-6)

How would I go about doing this problem?

Change in L = (alpha)Lo * change in T

You'll need to look up thermal expansion coefficients for glass and steel and solve for temp change where the final lengths are the same. Steel will have a higher (alpha)