Question

A 200 mm long, stress free rod at room temperature is held between two immovable rigid walls. The temperature of the rod is uniformly raised by ${250}^{o}C$. If the Young's modulus and coefficient of thermal expansion are 200 GPa and 1 x ${10}^{-5}{/}^{o}C$, respectively, the magnitude of the longitudinal stress (in MPa) developed in the rod is

• A. 500

Answer 1

The correct option is A 500
Given,

$l=200mm;\Delta T={250}^{o}C;\alpha =1\times {10}^{-5}{/}^{o}C$

$E=200GPa=200\times {10}^{3}MPa,\sigma =?$

$\sigma =\alpha \Delta TE={10}^{-5}\times 250\times 200\times {10}^3$ = 500 MPa