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Question

A steel scale measures the length of a copper rod as l0 when both are at 20oC, the calibration temperature for the scale. The scale reading when both are at 40oC, is

A
(1+20αC)l0
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B
(1+20αS)l0
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C
(1+20αS1+20αC)l0
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D
(1+20αC1+20αS)l0
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Solution

The correct option is D (1+20αC1+20αS)l0
lo is the reading at 20oC.
Let l1 be the scale reading at 20oC which gets aligned with the scale at 40oC.
At 40oC, length of the scale is lo(1+20αc)
The aligned reading on scale is l1(1+20αs)
So lo(1+20αc)=l1(1+20αs)
l1=(1+20αc1+20αs)lo

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