Question

The length of a metal rod at ${10}^{\circ }C$ is 1 m. Its coefficient of linear expansion is $12\times {10}^{-6}{/}^{\circ }C$.The temperature to which it must be heated so that the expansion in it is 12 mm is

• A. ${1000}^{\circ }C$
• B. ${820}^{\circ }C$
• C. ${1010}^{\circ }C$
• D. ${101}^{\circ }C$

Answer 1

Answer: (C)

${1010}^{\circ }C$

Rise in temperature $=$ change in length /( initial length X coefficient of linear expansion)
Here, change in length $=$ 12mm $=$ 12 X ${10}^{-3}m$
Initial length $=$ 1 m
$\alpha =12X{10}^{-6}$
Putting all the values we get raise in temperature $=$ 1000 degree centigrade.
So the final temperature should be 1010 degree centigrade