Heat and Thermal ExpansionEasy

Question

A bimetallic strip is formed out of two identical strips - one of copper and the other of brass. The coefficients of linear expansion of the two metals are αC and αB. On heating, the temperature of the strip goes up by ᐃT and the strip bends to form an arc of radius of curvature R. Then, R is

Options

A.proportional to ᐃT
B.inversely proportional to ᐃT
C.proportional to |αB - αC|
D.inversely proportional to |αB - αC|

Solution

          
Let l0 be the initial length of each strip before heating.
Length after heating will be
lB = l0(1 + αB ᐃT) = (R + d)θ
and lC l0(1 + αC ᐃT) = Rθ
∴
∴ = 1 + (αB - αC)ᐃT     [From binomial expansion]
∴
or   

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