Question

A metal rod having linear expansion coefficient 2 $\times {10}^{-5}°C^{-1}$ has a length of 1 m at ${20}^{\circ }$C. The temperature at which it is shortened by 1 mm is

• A. –20°C
• B. –15°C
• C. –30°C
• D. –25°C

Answer 1

The correct option is C –30°C

From, $I_2$ = $I_1$ [ 1 + $\alpha (t_2-t_1)$]
$t_2$ = $t_1+\frac{I_2-I_1}{I_1\alpha }$
= 20 + $\frac{-{10}^{-5}}{1.0\times 2\times {10}^{-5}}$ = -${30}^0$C