Q 11-08-100JEE MainJEE Main 2019 (12 Apr, Shift 2)Medium
A uniform cylindrical rod of length $L$ and radius $r$, is made from a material whose Young's modulus of elasticity equals $Y$. When this rod is heated by temperature $T$ and simultaneously subjected to a net longitudinal compressional force $F$, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equal to:
Answer: (D) $3F/(\pi r^2YT)$
The compressive strain cancels the thermal strain:
$$\frac{F}{\pi r^2Y} = \alpha T \Rightarrow \alpha = \frac{F}{\pi r^2YT}$$
$$\gamma = 3\alpha = \frac{3F}{\pi r^2YT}$$
Solution by Sreeraj P, M.Sc Physics