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 increases by $\Delta T$ and the strip bends to form an arc of radius $R$. Then $R$ is proportional to

• A. $\Delta T$
• B. $\frac{1}{\Delta T}$
• C. $\sqrt{\Delta T}$
• D. $\frac{1}{\sqrt{\Delta T}}$

Answer 1

Answer: (B)

Let $L_{0}$ be the initial length of each strip before heating.
Length after heating will be

$L_{B}=L_{0}\left(1+\alpha_{B} \Delta T\right)$
$=(R+d) \theta$
$L_{C}=L_{0}\left(1+\alpha_{C} \Delta T\right)=R \theta$
$\Rightarrow \frac{R+d}{R}=\frac{1+\alpha_{B} \Delta T}{1+\alpha_{C} \Delta T}$
$R=\frac{d}{R}=1+\left(\alpha_{B}-\alpha_{C}\right) \Delta T$
$R \propto \frac{1}{\Delta T}$