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# A metal rod has a length of 1m at ${30}^{0}C$ ,  $\text{'}\alpha \text{'}$ of metal is  $2.5×{10}^{-5}{/}^{0}C$, the temperature at which it will be shortened by 1mm is

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a
−300C
b
−400C
c
−100C
d
100C
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detailed solution

Correct option is C

coefficient of linear expansion of solid isα=ΔllΔthere Δl =-1mm=-10-3m=decrease in lengthl is initial length=1m; Δt is change in temperature;initial temperature = 300C; α=2.5x10-5/C  0     substitute given values in above equation2.5×10−5=−10−31×t2−30t2−30=−12.5×10−2=−1002.5t2−30=−40t2=−40+30=−100C=temperature at which rod will be shortened

Similar Questions

The coefficient of linear expansion of brass and steel are ${\mathrm{\alpha }}_{1}$ and ${\alpha }_{2}$. If we take a brass rod of length ${l}_{1}$ and steel rod of length ${l}_{\mathit{2}}$ at 0oC, their difference in length $\left({l}_{2}-{l}_{1}\right)$will remain the same at all temperatures if

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