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 ∆T and the strip bends to form an arc of radius of curvature R. Then R is :(i) proportional to ∆$$T(ii)$$ inversely proportional to ∆$$T(iii)$$ proportional to α$$B-$$α$$C(iv)$$ inversely proportional to α$$B-$$αC

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 ∆T and the strip bends to form an arc of radius of curvature R. Then R is :(i) proportional to ∆$$T(ii)$$ inversely proportional to ∆$$T(iii)$$ proportional to α$$B-$$α$$C(iv)$$ inversely proportional to α$$B-$$αC

Infinity Learn · Accepted Answer

Length of brass rod $$LB=Lo(1+$$αB∆$$T)=(R+d)$$θ  Length of copper rod $$LC=Lo(1+$$αc∆$$T)$$      $$=(R-d)$$θ ⇒$$R+dR-d=1+$$αB∆$$T1+$$αC∆T ⇒$$2R2d=2+($$α$$B+$$α$$C)$$∆$$T($$α$$B-$$α$$C)$$∆T Since   $$($$α$$B+$$α$$C)$$∆T <<<$$2$$ ∴  $$R=2d($$α$$B-$$α$$C)$$∆T.

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