An aluminium measuring rod, which is correct at 5∘C measures the length of a line as 80cm at 45∘C. If thermal coefficient of linear expansion of aluminium is 2.50×10−5/∘C, the correct length of the line is
A
80.08cm
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B
79.92cm
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C
81.12cm
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D
79.62cm
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Solution
The correct option is A80.08cm Given,
Length measured by aluminium rod at 5∘C is 80cm.....(1)
We know from the definition of linear expansion of a material for a small change in temperature ΔT ΔL=LαΔT......(2)
From the data given in the question,
the change in temperature of the material (ΔT)=45−5=40∘C
Using this in (2), we get
The increase in length ΔL=αAlLAlΔT=(2.50×10−5)×80×40 =0.08cm....(3)
Since length of the scale increases from the calibrated length at 5∘C,
The correct length of the line L=80+0.08=80.08cm
Hence, option (a) is the correct answer.