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A steel tape measures the length of a copper rod as 80.00 cm when at $15^{0} C$ , which is the calibration temperature for the tape. The reading of the tape (in cm) when both are at a temperature of $65^{0} C$ will be (linear expansivities of steel and copper are $12 \times 10^{- 6} / {}^{0}C$ respectively)

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answer is 80.02.

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Detailed Solution

$l'_{c} = l_{c} (1 + α_{c} Δ T); l'_{s} = l_{s} (1 + α_{c} Δ T); ∵ l'_{c} = l'_{s} \Rightarrow l_{s} (1 + 12 \times 10^{- 6} \times 50) = 80 (1 + 17 \times 10^{- 6} \times 50) ∴ l_{s} = 80.02 cm$

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