Question

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 DT and the strip bends to form an arc of radius of curvature R. Then R is

• A. Proportional to DT
• B. Inversely proportional to DT
• C. Proportional to |α_B − α_C|
• D. Inversely proportional to |α_B − α_C|

Answer 1

Answer: (B), (D)

The correct options are
B

Inversely proportional to DT

D

Inversely proportional to |α_B − α_C|

Let $L_0$ be the initial length of each strip before heating.

Length after heating will be

$L_B=L_0(1+{\alpha }_B△T)=(R+d)\theta$

$L_C=L_0(1+{\alpha }_C△T)=R\theta$

$\Rightarrow \frac{R+d}{R}=\frac{1+{\alpha }_B△T}{1+{\alpha }_C△T}$

$\Rightarrow 1+\frac{d}{R}=1+({\alpha }_B-{\alpha }_c)△T$

$\Rightarrow R=\frac{d}{({\alpha }_B-{\alpha }_c)△T}\Rightarrow R\propto \frac{1}{△T}andR\propto \frac{1}{({\alpha }_B-{\alpha }_C)}$