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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| 

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1 Answer

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by (519 points)

Let lbe the initial length each strip before heating

lb​=l0(1+αb​ΔT)
l​c=l0(1+αc​ΔT)
lc​=Rθ
lb​+(R+d)θ
Thus (R+d​)/R=1+αbΔT/1+αcΔT​
or 1+d/R​=1+(αb​−αc​)ΔT

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