What Temperature Allows a Brass Plug to Fit into an Iron Ring?

[davidkis]

Homework Statement

A brass plug is to be placed in a ring made of iron. At room temperature (20°C), the diameter of the plug is 8.764 cm and that of the inside of the ring is 8.754 cm. They must both be brought to what common temperature in order to fit?

Homework Equations

Change in V=B*V0*Change in T
B for brass = 56x10^-6
B for Iron = 35 x 10^-6

The Attempt at a Solution

I had no idea how to start i notice that the change in the coefficient of expansion is going to change the items dimensions but i honestly don't know where to begin, do i combine the 2 separate formulas? how would i solve for the temperture?

 

[rl.bhat]

Here you need not consider the volume expansion. Brass plug will pass through iron ring if their radii are the same.
Rb = Rb0( 1 + αb*Δt)
Ri = Ri0( 1 + αi*Δt)
where α is the coefficient of linear expansion which is equal to B/3.
Equate Rb and Ri and solve for Δt