Question

When a rod is heated but prevent from expanding, stress developed is independent of

• A. Material of the rod
• B. Rise in temperature
• C. Length of rod
• D. None of above

Answer 1

The correct option is C Length of rod

Let rise in temperature of the rod be $\Delta T$

The change in the length of the rod is given as:

$L=L_O(1+\alpha \Delta T)$

$\Delta L=L_O\alpha \Delta T$

$\frac{\Delta L}{L_O}=\epsilon =\alpha \Delta t$ ...(1)

Using the relation between stress and strain

$\sigma =Y\times \epsilon$

$\sigma =Y\times \left(\alpha \Delta t\right)$

$\sigma =Y\alpha \Delta t$

Option $\left(c\right)$ is correct