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When a metal rod is cooled from $500^{0} C$ to $0^{0} C$ , the density increases by 1.027 times. Then for the material

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The coefficient of linear expansion is $18 \times 10^{- 6}^{0} C^{- 1}$

The coefficient of linear expansion is $12 \times 10^{- 6}^{0} C^{- 1}$

The coefficient of Areal expansion is $36 \times 10^{- 6}^{0} C^{- 1}$

The coefficient of Areal expansion is $24 \times 10^{- 6}^{0} C^{- 1}$

answer is A, C.

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Detailed Solution

$γ = \frac{d_{o} - d_{t}}{d t (t_{2} - t_{1})}; t_{1} = 0^{o} C$ , $t_{2} = 500^{0} C$

$= \frac{1.027 - 1}{1 \times 500}$

$= \frac{0.027}{500}$

$\Rightarrow α = \frac{γ}{3} = \frac{0.027}{3 \times 500} = 18 \times 10^{- 6}^{0} C^{- 1}$

$β = 2 α = 36 \times 10^{- 6}^{0} C^{- 1}$

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