Question

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 its is :

• A. $\frac{Y}{\alpha t}$
• B. $Y\alpha t$
• C. $\frac{1}{\left(Y\alpha t\right)}$
• D. $\frac{\alpha t}{Y}$

Answer 1

Answer: (B)

$Y\alpha t$

Answer 2

$\frac{\Delta\ell}{\ell} = \alpha.\Delta T$ and $\quad Y = \frac{F/ A}{\Delta\ell/\ell}$ So,$\quad F = AY\alpha t$ Thermal stress $\left(\frac{F}{A}\right) = Y\alpha t.$