Question

At ${15}^{\circ }C$ the height of Eifel tower is $324m$. If it is made of iron, what will be the increase in length in cm, at ${30}^{\circ }C$? ( Take coefficient of linear expansion of Iron as $11.5\times {10}^{-6}{}^{\circ }{C}^{-1})$

• A. $5.6cm$
• B. $12.2cm$
• C. $2.4cm$
• D. $8.4cm$

Answer 1

The correct option is A $5.6cm$

Increase in length due to change in temperature is given as,
$\Delta l=\lambda l(T_2-T_1)$
where, $\lambda$ is the coefficient of linear expansion of solid, $l$ is the original length, $T_1$ is the initial temperature and $T_2$ is the final temperature.
Given, $l=324m$, $T_1={15}^{\circ }C$, $T_2={30}^{\circ }C$ and $\lambda =11.5\times {10}^{-6}$
$\Rightarrow \Delta l=11.5\times {10}^{-6}\times 324\times (30-15)$
$\Rightarrow \Delta l=5.6\times {10}^{-2}m=5.6cm$