Question

A horizontal steel railroad track has a length of 100 m when the temperature is ${25}^{o}C$. The track is constrained from expanding or bending. The stress on the track on a hot summer day, when the temperature is ${40}^{o}C$, is (Note: The linear coefficient of thermal expansion for steel is $1.1\times {10}^{-5}{/}^{o}C$ and the Youngs modulus of steel is $2\times {10}^{11}$ Pa)

• A. $6.6\times {10}^{7}Pa$
• B. $8.8\times {10}^{7}Pa$
• C. $3.3\times {10}^{7}Pa$
• D. $5.5\times {10}^{7}Pa$

Answer 1

Answer: (C)

$3.3\times {10}^{7}Pa$

Young modulus of the steel is given by

$\frac{F}{A}=Y\alpha \Delta T=2\times {10}^{11}\times 1.1\times {10}^{-5}\times 15$
$=3.3\times {10}^{7}Pa$