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A steel scale is error-less at 50^(@)F. ...

A steel scale is error-less at `50^(@)F`. Using the scale, the length of a brass rod is found to be 1.5 m at `50^(@)C`. What is the true length of the rod at `100^(@)C`? (Coefficients of linear expansion of steel and brass are `11.2 times 10^(-6@)C^(-1) " and " 18 times 10^(-6@)C^(-1)` respectively.)

Text Solution

Verified by Experts

Let `50^(@)F` be equal to `t^(@)C`, so that `t/5=(50-32)/9` i.e., t=10. Hence, the steel scale is error-less at `10^(@)C.`
Therefore the true of 1 m, measured at `50^(@)C`, should be
`" " l=1{1+11.2 times 10^(-6) times (50-10)}`
`" " =1+11.2 times 10^(-6) times 40=1.000448 m`
`therefore` The true length of measured 1.5 m of the brass rod at `50^(@)C=1.5 times 1.000448=1.5007m`.
`therefore` The true of the brass rod at `100^(@)C`
`" " =1.5007{1+0.000018(100-50)}`
`" " =1.5007{1+0.000018 times 50}=1.502m.`
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