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Two metal rods are fixed end to end between two rigid supports as shown in figure. Each rod is of length l and area of cross –section is A. When the system is heated up, determine the condition when the junction between rods does not shift?
(Given : $Y_{1} and Y_{2}$ are Young’s modulus of material of the rods, $α_{1} and α_{2}$ are coefficients of linear expansion)

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$Y_{1} = Y_{2}$

$Y_{1} \sqrt{α_{1}} = Y_{2} \sqrt{α_{2}}$

$Y_{1} α_{1} = Y_{2} α_{2}$

$Y_{1} α_{1} = Y_{2} α_{1}$

answer is A.

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Detailed Solution

when forces developed is same, shift is zero

$Y_{1} A_{1} α_{1} (∆ θ) = Y_{2} A_{2} α_{2} (∆ θ) \Rightarrow Y_{1} α_{1} = Y_{2} α_{2}$

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