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The length of a metal rod at $0^{0} C$ is 0.5m. When it is heated, its length increases by 2.7mm. The final temperature of rod is (coefficient of linear expansion of metal = $90 \times 10^{- 6} /^{0} C)$

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$20^{0} C$

$30^{0} C$

$40^{0} C$

$60^{0} C$

answer is D.

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Detailed Solution

Linear expansion of a rod is given by

$∆ L = Lα ∆ T$

$∆ T = \frac{∆ L}{Lα} = \frac{2.7 \times 10^{- 3}}{0.5 \times 90 \times 10^{- 6}} = 60^{0}$

$\Rightarrow T_{2} - 0^{0} = 60^{0} \Rightarrow T_{2} = 60^{0}$

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