Question

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

• A. $-20^\circ C$
• B. $-15^\circ C$
• C. $-30^\circ C$
• D. $-25^\circ C$

Answer 1

Answer: (C)

From, $l_{2}=l_{1}\left[1 + \alpha \left(t_{2} - t_{1}\right)\right]$
$t_{2}=t_{1}+\frac{l_{2} - l_{1}}{l_{1} \alpha }$
= $20+\frac{- 10^{- 3}}{1 .0 \times 2 \times 10^{- 5}}=-30^\circ C$