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Question
Two metallic strips each of thickness 10−4 m are riveted together. Their coefficients of linear expansion are 10−5 ∘C−1 and 2×10−5 ∘C−1. If they are heated through a temperature change of 50 ∘C, the bimetallic strip will bend to form an arc of radius
Two metallic strips each of thickness 10−4 m are riveted together. Their coefficients of linear expansion are 10−5 ∘C−1 and 2×10−5 ∘C−1. If they are heated through a temperature change of 50 ∘C, the bimetallic strip will bend to form an arc of radius
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Solution
The correct option is B 20 cm
Given:
Thickness of metallic strips, t=10−4 m
Coefficient of linear expansion of strip 1, α1=10−5 ∘C−1
Coefficient of linear expansion of strip 2, α2=2×10−5 ∘C−1
Temperature change, ΔT=50 ∘C
To find:
Radius of arc of bimetallic strip, r=?
We know that, radius of arc is given by
r=t(α2−α1)ΔT
⇒r=10−4(2×10−5−10−5)×50
⇒r=0.2 m=20 cm
Given:
Thickness of metallic strips, t=10−4 m
Coefficient of linear expansion of strip 1, α1=10−5 ∘C−1
Coefficient of linear expansion of strip 2, α2=2×10−5 ∘C−1
Temperature change, ΔT=50 ∘C
To find:
Radius of arc of bimetallic strip, r=?
We know that, radius of arc is given by
r=t(α2−α1)ΔT
⇒r=10−4(2×10−5−10−5)×50
⇒r=0.2 m=20 cm
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