Question

A metal rod having a linear coefficient of expansion $2\times {10}^{-5}{/}^{\circ }$C has a length 1 m at ${25}^{\circ }$C, the temperature at which it is shortened by 1 mm is :

• A. ${50}^{\circ }$C
• B. $-{50}^{\circ }$C
• C. $-{25}^{\circ }$C
• D. $-{12.5}^{\circ }$C

Answer 1

The correct option is C $-{25}^{\circ }$C

We know, $\alpha =\frac{dl}{l\times dt}$ where $dl=$ change in length and $l=$ initial length and $dt=$ change in temperature.

So, $dt=\frac{dl}{l\times \alpha }$

In this case, $\alpha =2\times {10}^{-5}$/${}^{\circ }$ C

$l=1$ m

$t={25}^0$ C

$dl=1mm=1\times {10}^{-3}$ m

Putting these values we get, $dt=50$/ ${}^{\circ }$C

Since present temperature $={25}^{\circ }$ C

The final temperature should be $-{25}^{\circ }$C