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The difference in length of two metal ro...

The difference in length of two metal rods A and B is 25 cm at all temperatures. Coefficients of linear expansion of the materials of A and B are `1.28 times 10^(-5@)C^(-1) " and " 1.92 times 10^(-5@)C^(-1)` respectively. Find the length of each rod at `0^(@)C`.

Text Solution

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Let `l_(A) " and " l_(B)` be the lengths of the rods A and B respectively at `0^(@)C`.
From the given condition, increase in length of rod A due to `t^(@)C` rise in temperature = increase in length of rod B due to the same rise in temperature.
`therefore " " l_(A) times 1.28 times 10^(-5) times t=l_(B) times 1.92 times 10^(-5) times t`
`therefore " " 2l_(A)=3l_(B) " or, " l_(A)=3/2l_(B)`
`because " " l_(A) gt l_(B),`
`" " l_(A)-l_(B)=25 " or, " 3/2l_(B)-l_(B)=25`
or, `" " l_(B)=50cm.`
`therefore " " l_(A)=3/2l_(B)=3/2 times 50=75cm`.
`therefore` Length of rod A at `0^(@)C` is 75 cm, and that of rod B at `0^(@)C` is 50 cm.
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