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An aluminium measuring rod which is correct at $5 ° C$ measures the length of a line as 80 cm at $45 ° C .$ If thermal coefficient of linear expansion of aluminium is $2.50 \times 10^{- 5} / ° C,$ the correct length of the line is

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$79.62 c m$

$81.12 c m$

$80.08 c m$

$79.92 c m$

answer is A.

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Detailed Solution

Increase in length $Δ L = L \propto Δ θ = 80 \times 2.50 \times 10^{- 5} \times (45 - 5) ≃ 0.08 c m$

$∴$ The correct length of the line $= 80 + .08 = 80.08 c m$

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