Q 11-08-104JEE MainJEE Main 2017 (9 Apr)Easy
A steel rail of length $5$ m and area of cross section $40\ \text{cm}^2$ is prevented from expanding along its length while the temperature rises by $10^\circ$C. If coefficient of linear expansion and Young's modulus of steel are $1.2\times10^{-5}\ \text{K}^{-1}$ and $2\times10^{11}\ \text{N m}^{-2}$ respectively, the force developed in the rail is approximately:
Answer: (D) $1\times10^5$ N
The prevented thermal strain is $\alpha\,\Delta T$, so
$$F = YA\alpha\,\Delta T = 2\times10^{11}\times40\times10^{-4}\times1.2\times10^{-5}\times10 = 9.6\times10^4\ \text{N} \approx 1\times10^5\ \text{N}$$
(The length does not matter.)
Solution by Sreeraj P, M.Sc Physics