Thermal properties of Matter

Question

A bimetallic strip is formed out of two identical strips, one of Cu and the other of brass. The coefficients of linear expansion of the two metals are αc​ and αb​. If on heating the temperature of the strip goes up by ΔT and the strip bends to form an arc of radius R, then R is

A)   proportional to ΔTΔT

B)    inversely proportional to ΔTΔT

C)    proportional to |αB−αC|

D)    inversely proportional to |αB−αC| 

Answer 1

Let l₀ be the initial length each strip before heating

l_b​=l₀(1+αb​ΔT)
l​_c=l₀(1+αc​ΔT)
l_c​=Rθ
l_b​+(R+d)θ
Thus (R+d​)/R=1+α_bΔT/1+α_cΔT​
or 1+d/R​=1+(αb​−αc​)ΔT