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An iron rod of length 50cm is joined at ...

An iron rod of length 50cm is joined at an end to copper rod of length 100cm at `20^(@)C`. Find the length of the system at `100^(@)C` and average coefficient of linear expansion of the system.
`(alpha_("iron")=12xx10^(-6)//""^(@)Candalpha_("copper")=17xx10^(-6)//""^(@)C.)`

Text Solution

Verified by Experts

Increase in length of combined rod = increase in length of iron rod + Increase in length of copper rod
`(Delta l) = (Delta l )_(Fe) + (Delta l)_(Cu)`
`(l_(Fe) + l_(Cu)) prop_("Avg") Delta t = l_(Fe ) prop_(Fe) Delta + l_(Cu) prop_(Cu) Delta t`
`prop_("Aug") = (l_(Fe) prop_(Fe) +l_(Cu) prop_(Cu))/((l_(Fe) + l_(Cu)))`
`= (50 xx 12 xx 10^(-6) + 100 xx 17 xx 10^(-6))/(150) = 15.33 xx 10^(-6) //^(0)`C
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