First slide

Thermal expansion

Question

Three rods of equal length are joined to form an equilateral triangle ABC. D is midpoint of AB. Coefficient of linear expansion of AB is $α_{1} and α_{2}$ for AC and BC. If distance DC remains constant for small changes is temperature, then

Moderate

A

$α_{1} = α_{2}$
B

$α_{1} = 2 α_{2}$
C

$α_{1} = 4 α_{2}$
D

$α_{2} = 4 α_{1}$

Solution

$\begin{array}{l} Δ l = l_{1} α Δ t \\ {(D C)}^{2} = {(A C)}^{2} - {(A D)}^{2} \\ = l^{2} - {(\frac{l}{2})}^{2} \end{array}$

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