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 ${\alpha }_{c}and{\alpha }_s$. On heating, the temperature of the strip goes up by$\Delta$T 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.
• D.

Answer 1

Answer: (B), (D)

The correct options are
B

Inversely proportional to DT

D

let $L_0$ be the initial length of each strip before heating.
Length after heating will be
$L_B=L_0(1+{\alpha }_B△T)=(R+d)\theta$

$L_c=L_0(1+{\alpha }_C△T)=R\theta$
$\Rightarrow \frac{R+d}{R}=\frac{1+{\alpha }_B△T}{1+{\alpha }_C△T}$
$\Rightarrow 1+\frac{d}{R}=1+({\alpha }_B-{\alpha }_C)△T$
$\Rightarrow R=\frac{d}{({\alpha }_B-{\alpha }_C)△T}\Rightarrow R\propto \frac{1}{△T}And$
$R\propto \frac{1}{({\alpha }_B-{\alpha }_C)}$