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Three rods of equal lengths are joined to form an equilateral triangle ABC. D is the mid point of AB. The coefficient of linear expansion in $α_{1}$ for material of rod AB and BC. $α_{2}$ for material of rod AC. If the distance DC remains constant for small changes in temperature. Then

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$α_{1} = 2 α_{2}$

$α_{1} = 8 α_{2}$

$α_{1} = α_{2}$

$α_{1} = 4 α_{2}$

answer is B.

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Detailed Solution

$C D^{2} = A C^{2} - A D^{2}$ $l^{2} - \frac{l^{2}}{4} = C D^{2}$ at $θ_{1} {}^{0}C$

$l^{2} {(1 + α_{2} θ)}^{2} - \frac{l^{2}}{4} (1 + 2 α_{1} θ + α_{1}^{2} θ^{2}) = C D^{2} a t θ_{2} {}^{0}C$

by simply fying above equation $α_{1} = 4 α_{2}$

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