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Question
A thin brass sheet at 10∘ C and thin steel sheet at 20∘ C have the same surface area.The common temperature at which both would have the same area : (Coefficient of linear expansion for brass and steel are respectively 19×10−6/∘C and 11×10−6/∘C.)
A thin brass sheet at 10∘ C and thin steel sheet at 20∘ C have the same surface area.The common temperature at which both would have the same area : (Coefficient of linear expansion for brass and steel are respectively 19×10−6/∘C and 11×10−6/∘C.)
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Solution
The correct option is D −3.75∘C
αb=19×10−6/∘ C So, βb=38×10−6/∘C
αS=11×10−6/∘C So, βS=22×10−6/∘C
Now, we know, A2=A1(1+βdt), where dt = change in temperature
Let the common temperature at which the plates will have same area be t,
Then,
Ab=A0(1+βb(t−10))
and
AS=A0(1+βS(t−20))
βb(t−10)=βs(t−20)
solving we get,
t=−3.75oC
αb=19×10−6/∘ C So, βb=38×10−6/∘C
αS=11×10−6/∘C So, βS=22×10−6/∘C
Now, we know, A2=A1(1+βdt), where dt = change in temperature
Let the common temperature at which the plates will have same area be t,
Then,
Ab=A0(1+βb(t−10))
and
AS=A0(1+βS(t−20))
βb(t−10)=βs(t−20)
solving we get,
t=−3.75oC
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