Question

A steel rail of length 5 m and area of cross section $40c{m}^2$ is prevented from expanding along its length while the temperature rises by ${10}^{o}C$. If coefficient of linear expansion and Young's modulus of steel are $1.2\times {10}^{-5}{K}^{-1}$ and $2\times {10}^{11}N{m}^{-2}$ respectively, the force developed in the rail is approximately :

• A. $2\times {10}^{7}N$
• B. $3\times {10}^{-5}N$
• C. $1\times {10}^{5}N$
• D. $2\times {10}^{9}N$

Answer 1

The correct option is C $1\times {10}^{5}N$

$YoungsmodulesY=2\times {10}^{11}N{m}^{-2}linearsexpressioncoefficient\propto =1.2\times {10}^{-5}{K}^{-1}l=5cmA=40c{m}^2\Delta T={10}^{\circ }C\Delta l=l\propto \Delta T\frac{\Delta l}{l}=\propto \Delta T[F=YA\frac{\Delta l}{l}]F=YA\propto \Delta TF=2\times {10}^{11}N{m}^{-2}\times \frac{40}{10}m\times 1.25\times {10}^{-5}\times 10=2\times 40\times 12\times {10}^2=96\times {10}^3=0.96\times {10}^{3}F\cong 1\times {10}^{5}N$