The coefficient of linear expansion of a rod of length 2m varies with distance x from end of the rod as $α = α_{0} + α_{1} x$ where $α_{o} = 1.5 \times 10^{- 5} /^{0} C, α_{1} = 2.5 \times 10^{- 6} /^{0} C$ . Find the increase in length of the rod when heated through 350⁰C

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122.5 mm

1.225 mm

0.1225 mm

12.25 m

answer is C.

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Detailed Solution

$\begin{array}{l} α = \frac{1}{d x} \frac{d e}{d θ} \Rightarrow d e = α . d x \cdot d θ \Rightarrow \int de = \int_{0}^{2} α \cdot d x \cdot d θ \\ e = 350 \times \int_{0}^{2} (α_{0} + α_{1} x) d x = 12.25 mm \end{array}$

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