A thin brass sheet at 10∘C and a thin steel sheet at 20∘C have same surface area. The common temperature at which both would have the same area is :
Coefficient of areal expension for brass and steel are 10×10−6∘C−1 and 20×10−6∘C−1 respectively.
A
10∘C
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B
20∘C
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C
30∘C
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D
35∘C
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Solution
The correct option is C30∘C We know ,
Final area A=A0(1+βΔT)
where A0 is initial area.
Given: A0 is same for both brass and steel sheet at 10∘C and 20∘C respectively.
Let at temperature T, both have same area A. A0(1+βbΔT1)=A0(1+βsΔT2) A0(1+βb(T−10))=A0(1+βs(T−20)) βbβs=T−20T−10 ⇒10×10−6∘C−120×10−6∘C−1=T−20T−10 ⇒T=30∘C