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Two elastic rods are joined between fixed supports as shown in figure. Condition for no change in the lengths of individual rods with the increase of temperature \( \left(\alpha_{1}, \alpha_{2}=\right. \) linear expansion coefficient, \( A_{1} \) and \( A_{2}= \) area of rods, \( y_{1} \) and \( y_{2}= \) young modulus)
(A) \( \frac{A_{1}}{A_{2}}=\frac{\alpha_{1} y_{1}}{\alpha_{2} y_{2}} \)
(B) \( \frac{A_{1}}{A_{2}}=\frac{L_{1} \alpha_{1} y_{1}}{L_{2} \alpha_{2} y_{2}} \)
(C) \( \frac{A_{1}}{A_{2}}=\frac{L_{2} \alpha_{1} y_{1}}{L_{1} \alpha_{2} y_{2}} \)
(D) \( \frac{A_{1}}{A_{2}}=\frac{\alpha_{2} y_{2}}{\alpha_{1} y_{1}} \)
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