(A) The thermal expansion of the rod is given by $\Delta L = \alpha L \Delta T$,where $\Delta T = t$.Since the rod is held at both ends such that its

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(A) The thermal expansion of the rod is given by $\Delta L = \alpha L \Delta T$,where $\Delta T = t$.Since the rod is held at both ends such that its length remains invariant,the compressive strain produced is $\epsilon = \frac{\Delta L}{L} = \alpha t$.According to Hooke's Law,the stress $\sigma$ is related to strain $\epsilon$ by the Young's modulus $Y$ as $\sigma = Y \epsilon$.Substituting the value of strain,we get $\sigma = Y \alpha t$.Therefore,the linear stress developed in the rod is $Y \alpha t$.

Class 11 Physics Mechanical Properties of Solids Young’s Modulus

Medium

$A$ metal rod of Young's modulus $Y$ and coefficient of thermal expansion $\alpha$ is held at its two ends such that its length remains invariant. If its temperature is raised by $t^{\circ} C$,the linear stress developed in it is

AIEEE 2011 All AIEEE

A
$Y \alpha t$
B
$\frac{Y}{\alpha t}$
C
$\frac{\alpha t}{Y}$
D
$\frac{1}{Y \alpha t}$

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$A$ metal rod of Young's modulus $Y$ and coefficient of thermal expansion $\alpha$ is held at its two ends such that its length remains invariant. If its temperature is raised by $t^{\circ} C$,the linear stress developed in it is

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