Question

When a rod is heated but prevented from expanding the stress developed is independent of:

• A. material of the rod
• B. rise in temperature
• C. length of rod
• D. none of the above

Answer 1

Answer: (C)

length of rod

Answer 2

$L_{t}=L_{0}(1+\alpha \Delta \theta)$
$\Delta L=L_{t}-L_{0}=L_{0}\, \alpha \,\Delta \theta \ldots( i )$
If the same rod of length Lo is subjected to stress along its length, then extension in length can be calculated by Hooke's law.
$Y=\frac{\text { tress }}{\text { strain }}=\frac{\text { stress }}{\Delta L / L_{0}}$
$=\frac{L_{0} \times \text { stress }}{\Delta L}$
$\therefore \Delta L=\frac{L_{0} \times \text{stress}}{Y} ...(ii)$
If the rod is prevented by expanding, we have
$L_{0} \alpha \Delta \theta=\frac{L_{0} \times \text { stress }}{Y}$
$\therefore$ Stress $=Y \alpha \Delta \theta$
(independent of $\left.L_{0}\right)$