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 ${\alpha }_C$ 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 $R$ is

• A. Proportional to $△T$
• B. Inversely proportional to $△T$
• C. Proportional to $|{\alpha }_B-{\alpha }_C|$
• D. Inversely proportional to $|{\alpha }_B+{\alpha }_C|$

Answer 1

Answer: (B), (D)

The correct options are
B Inversely proportional to $△T$
D Inversely proportional to $|{\alpha }_B+{\alpha }_C|$

The expression of radius of curvature $R$ is
$R=\frac{d}{({\alpha }_1-{\alpha }_2)△t}$
Thus, $R\propto \frac{1}{△t}$ and $R\propto \frac{1}{|{\alpha }_B-{\alpha }_C|}$.