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 these

Answer 1

The correct option is C length of rod

$L_t=L_0(1+\alpha △\theta )$
$△L=L_t-L_0=L_0\alpha △\theta$
If the same rod of lenghth $L_0$ is subjected to stress along its length, then extension in length can be calculated by Hooke's law
$Y=\frac{stress}{strain}=\frac{stress}{\frac{△L}{L_n}}$
$=\frac{L_0\times stress}{△L}$
Therefore $△L=\frac{L_0\times stress}{Y}$
If the rod is prevented from expanding, we have
$L_o\alpha △\theta =\frac{L_o\times stress}{Y}$
Therefore stress$=Y\alpha △\theta$= (independent of $L_0)$