Q 11-08-094JEE MainJEE Main 2019 (9 Jan, Shift 1)Easy
A rod, of length $L$ at room temperature and uniform area of cross section $A$, is made of a metal having coefficient of linear expansion $\alpha/^\circ\text{C}$. It is observed that an external compressive force $F$ is applied on each of its ends, prevents any change in the length of the rod when its temperature rises by $\Delta T$ K. Young's modulus, $Y$ for this metal is
Answer: (C) $\dfrac{F}{A\alpha\Delta T}$
The force must cancel the free thermal expansion, so the compressive strain equals the thermal strain $\alpha\Delta T$ (a temperature difference is the same in K and $^\circ$C):
$$Y = \frac{F/A}{\alpha\Delta T} = \frac{F}{A\alpha\Delta T}$$
Solution by Sreeraj P, M.Sc Physics