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Two rods of different materials are clamped at their ends rigidly. When they are heated for the same rise in temperature, same thermal stresses are produced in them. If their Young's modulii are in the ratio $x : y$ then ratio of coefficients of their linear expansion is....

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$x : y$

$y : x$

$x^{2} : y^{2}$

$y^{2} : x^{2}$

answer is B.

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Detailed Solution

Thermal stress = $y α Δ t$

$y \propto \frac{1}{α} ⇒ \frac{α_{1}}{α_{2}} = \frac{Y_{2}}{Y_{1}} = \frac{y}{x}$

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