Question

A rod of length $l$ and radius $r$ is held between two rigid walls so that it is not allowed to expand. If its temperature is increased, then the force developed in it is proportional to

• A. $L$
• B. $1 / L$
• C. $r^{2}$
• D. $r^{-2}$

Answer 1

Answer: (C)

$(\Delta L)$ Thermal expansion $=L \propto \Delta Q$
Where $L=$ Length original
$\propto=$ Coeffcient of linear expansion
$\Delta Q=$ Change in temperature
Or we can say
$\Delta L \propto L$
And force required to produce similar elongation can be calculated by
$F=A Y \cdot \frac{\Delta L}{L} \,\,[\because Y$ is constant $]$
So $F \propto r^{2} \cdot \frac{\Delta L}{L}$
Also $\Delta L \propto L$
So $F$ only proportional to $r^{2}$