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Q.

There rods of equal lengths are joined to form an equilateral triangle ABC.D is the mid–point of AB. The coefficient of linear expansion is α1 for material of rod AB and BC, α2. For material of rod AC. If the distance DC remains constant for small changes in temperature, then

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a

$α_{1} = 2 α_{2}$

b

$α_{1} = 4 α_{2}$

c

$α_{1} = 8 α_{2}$

d

$α_{1} = α_{2}$

answer is B.

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Detailed Solution

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${CD}^{2} = {AC}^{2} - {AD}^{2} l^{2} - \frac{l^{2}}{4} = {[l (1 + α_{2} θ)]}^{2} - {(\frac{l}{2} (1 + α_{1} θ))}^{2} = l^{2} [1 + 2 α_{2} θ + α_{2}^{2} θ^{2}] - \frac{l^{2}}{4} [1 + 2 α_{1} θ + α_{1}^{2} θ^{2}] By simplifying we get α_{1} = 4 α_{2}$

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