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 αC and αB . 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 |αBαC|

D) Inversely proportional to |αBαC|

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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 LB=L0(1+αBΔT)=(R+d)θ

LC=L0(1+αCΔT)=Rθ

therefore R+dR=1+αBΔT1+αCΔT

therefore 1+dR=1+(αBαC)ΔT

therefore R=d(αBαC)ΔT

therefore R1ΔT and R1(αBαC)



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