Thermometry Calorimetry And Thermal Expansion 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}}| $
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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 $ Þ $ \frac{R+d}{R}=\frac{1+{\alpha_{B}}\Delta T}{1+{\alpha_{C}}\Delta T} $ Þ $ 1+\frac{d}{R}=1+({\alpha_{B}}-{\alpha_{C}})\Delta T $ Þ $ R=\frac{d}{({\alpha_{B}}-{\alpha_{C}})\Delta T} $ Þ $ R\propto \frac{1}{\Delta T} $ and $ R\propto \frac{1}{({\alpha_{B}}-{\alpha_{C}})} $
BETA
