One way to construct a device with two points whose separation remains the same in spite of

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One way to construct a device with two points whose separation remains the same in spite of temperature changes is to bolt together one end of two rods having different coefficients of linear expansion as in the arrangement shown in figure.

(a) Show that the distance L will not change with temperature if the lengths LA and LB are chosen such that LA/LB = aB/aA.

(b) If material B is steel, material A is brass, and LA = 250 cm at 0oC, what is the value of L?

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