Question

A concrete railroad tie has a length $2.45m$ on a hot sunny day having temperature $35{}^{\circ }C$. What is the length of the railroad tie in the winter when the temperature dips to $-25{}^{\circ }C$? (Take the coefficient of linear expension of railroad as $12\times {10}^{-5}/{}^{\circ }C$)

• A. $1.8\times {10}^{-3}m$
• B. $1.2\times {10}^{-3}m$
• C. $1.5\times {10}^{-3}m$
• D. $2.4\times {10}^{-3}m$

Answer 1

The correct option is A $1.8\times {10}^{-3}m$

First find the change in the tie's length,
$\Delta l=\alpha l\Delta T$
where, $\Delta l$ is the change in length, $\alpha$ is the coefficient of linear expansion, $l$ is the original length and $\Delta T$ is the change in temperature.
or, $\Delta l=(12\times {10}^{-5})\times \left(2.45\right)\times (-25-35))$
or, $\Delta l=-0.0018m$