A bimetallic strip is formed out of two identical strips, one of copper and other of brass. The coefficients of linear expansion of the two metals are ${\alpha }_c$ and ${\alpha }_b$. On heating, the temperature of the strip goes up by $∆$T and the strip bends to form an arc of radius of curvature R. Then, which of the following statement is correct about the radius of curvature?

detailed solution

Correct option is B

Let L0 be the initial length of each strip before heating.Length after heating will be                       Lb = L0 (1+αb∆T) = (R+d)θ                                        …(i)                                                    (∵Length of an arc = Radius × Angle)                                  Lc = L0 (1 + αc∆T) = Rθ                                     …(ii)On dividing Eq. (i) by Eq. (ii), we get⇒  R+dR=1+αbΔT1+αcΔT⇒1+dR=1+αb-αcΔT⇒            R=dαb-αcΔT⇒            R∝1ΔTand          R∝1αb-αc        i.e. R is inversely proportional to ∆T and (αb-αc).