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Question

An aluminium measuring rod, which is correct at 5C measures the length of a line as 80 cm at 45C. If thermal coefficient of linear expansion of aluminium is 2.50×105/C, the correct length of the line is

A
80.08 cm
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B
79.92 cm
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C
81.12 cm
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D
79.62 cm
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Solution

The correct option is A 80.08 cm
Given,
Length measured by aluminium rod at 5C is 80 cm .....(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)=455=40C
Using this in (2), we get
The increase in length
ΔL=αAlLAlΔT=(2.50×105)×80×40
=0.08 cm ....(3)
Since length of the scale increases from the calibrated length at 5 C,
The correct length of the line L=80+0.08=80.08 cm
Hence, option (a) is the correct answer.

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