An iron rod of length 50cm is joined at an end to copper rod of length 100 cm at 20^(0)C. Find the length of the system at 100^(0)C and average coefficient of linear expansion of the system. (alpha_(iron) = 12 xx 10^(-6)//^(0) C and alpha_("copper") = 17 xx 10^(-6)//^(0) C . )

An iron rod of length 50cm is joined at an end to copper rod of length

1.	An iron rod of length 50cm is joined at an end to copper rod of length 100 cm at 20^(0)C. Find the length of the system at 100^(0)C and average coefficient of linear expansion of the system. (alpha_(iron) = 12 xx 10^(-6)//^(0) C and alpha_("copper") = 17 xx 10^(-6)//^(0) C . )
Answer» Solution :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