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What should be the length of steel and c...

What should be the length of steel and copper rods at `0^(@)C` that the length of steel rod is 5 cm longer than copper at all termperature? Given `alpha_(Cu) = 1.7 xx 10^(5) .^(@)C^(-1)` and `alpha_(steel) = 1.1 xx 10^(5) .^(@)C^(-1)`.

A

9.17 cm , 14.17 cm

B

9.02 cm, 14.20 cm

C

9.08cm, 14.08 cm

D

9.50 cm,14.50 cm

Text Solution

Verified by Experts

Let `L_(s)` and `L_(c)` be the lengths of the steel and copper rods and `alpha_(s)` and `alpha_(c)` be their coefficients of linear expansion respectively. When the rods are heated by `Deltat^(@)C` the increase in the length of steeel rod and copper rod are
`DeltaL_(s)=L_(S)alpha_(S) Delta t`
`Delta L_(c)=L_(C) alpha_(C)Delta t`
Given `L_(S)-L_(C)=5 cm ` for all `Deltat`
`L_(S) alpha_(S) Delta t-L_(C) alpha_(C) Deltat`
`(L_(s))/(L_(C))=(alpha_(C))/(alpha_(S))=(1.7xx10^(-5))/(1.1xx10^(-5))`
`L_(S)=(17L_(C))/11` Using this in `L_(S)-L_(C)=5` and solving we get `L_(C)=9.17` cm
Therefore `L_(S)=5+9.17=14.4cm`
Hence A is correct.
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