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 $α_{C} and α_{B}$ . 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 R is :
(i) proportional to $∆ T$
(ii) inversely proportional to $∆ T$
(iii) proportional to $|α_{B} - α_{C}|$
(iv) inversely proportional to $|α_{B} - α_{C}|$

Question

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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