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Q.

A steel scale measures the length of a copper rod as L cm when both are at 20oC, the calibration temperature for the scale. If the coefficients of linear expansion for steel and copper are αs and αcrespectively, what would be the scale reading (in cm) when both are at 27oC ?

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a

L

b

Lαs/αc

c

Lαcαs

d

L1+αc1+αs

answer is D.

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Detailed Solution

Length of 1 cm division of steel scale at 21oC is(1cm)1+αs(21−20)=1+αscmLength of copper rod at 21oC will beL×1×αC(21−20)=L1+αCcm∴Scale reading at 21oC will beL1+αc1+αscm

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