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Question

A metal rod having a linear coefficient of expansion 2×105/C has a length 1 m at 25C, the temperature at which it is shortened by 1 mm is :

A
50C
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B
50C
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C
25C
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D
12.5C
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Solution

The correct option is C 25C
We know, α=dll×dt where dl= change in length and l= initial length and dt= change in temperature.

So, dt=dll×α

In this case, α=2×105/ C

l=1 m

t=250 C

dl=1mm=1×103 m

Putting these values we get, dt=50/ C

Since present temperature =25 C

The final temperature should be 25C

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