Question

A steel rail of length $5\,m$ and area of cross section 40 $cm^2$ 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 $1.2 \times 10^{-5} \, K^{-1}$ and $2 \times 10^{11} \, Nm^{-2}$ respectively, the force developed in the rail is approximately :

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

Answer 1

Answer: (B)

$1 \times 10^5 N$

Answer 2

$F=yA\, \infty \,\Delta t$
$=2\times10^{11}\times 40\times 10^{-4}\times 1.2\times 10^{-5}\times 10$
$=9.6\times 10^{4}=1\times 10^{5}$ N