Question

A circular metallic rod of length 250 mm is placed between two rigid immovable walls as shown in the figure. The rod is perfect contact with the wall on the left side and there is a gap of 0.2 mm between the rod and the wall on the right side. If the temperature of the rod is increased by ${200}^{o}C$, the axial stress developed in the rod is _____ MPa.
Young's modulus of the material of the rod is 200 GPa and the coefficient of thermal expansion is ${10}^{-5}pe{r}^{o}C$

• A. 240

Answer 1

The correct option is A 240
Free expansion of rod $=L\alpha \Delta T$

$=250\times {10}^{-5}\times 200=0.5mm$

Actual expansion = 0.2 mm

$\therefore$ Expansion resisted = 0.3 mm

$\therefore Strainresisted=\frac{0.3}{250}$

$Stressdeveloped=\frac{0.3}{250}\times 200\times {10}^3$

$=0.24\times {10}^3=240MPa$