Properties Of Solids And Liquids Question 100
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 [IIT-JEE (Screening) 1999]
Options:
A) Proportional to DT
B) Inversely proportional to DT
C) Proportional to $ |{\alpha _{B}}-{\alpha _{C}}| $
D) Inversely proportional to $ |{\alpha _{B}}-{\alpha _{C}}| $
Show Answer
Answer:
Correct Answer: D
Solution:
Let L0 be the initial length of each strip before heating.
Length after heating will be $ L _{B}=L _{0}(1+{\alpha _{B}}\Delta T)=(R+d)\theta $
$ L _{C}=L _{0}(1+{\alpha _{C}}\Delta T)=R\theta $
therefore $ \frac{R+d}{R}=\frac{1+{\alpha _{B}}\Delta T}{1+{\alpha _{C}}\Delta T} $
therefore $ 1+\frac{d}{R}=1+({\alpha _{B}}-{\alpha _{C}})\Delta T $
therefore $ R=\frac{d}{({\alpha _{B}}-{\alpha _{C}})\Delta T} $
therefore $ R\propto \frac{1}{\Delta T} $ and $ R\propto \frac{1}{({\alpha _{B}}-{\alpha _{C}})} $
