A composite rod is made by joining a copper rod, end to end, with a second rod of different material but of the same area of cross section. At `25^(@)C`, the composite rod is `1 m` long and the copper rod is `30 cm` long. At `125^(@)C` the length of the composte rod increases by `1.91 mm`. When the composite rod is prevented from expanding by bolding it between two rigid walls, it is found that the constituent reds have remained unchanged in length in splite of rise of temperature. Find yong's modulus and the coefficient of linear expansion of the second red (Y of copper `=1.3xx10^(10) N//m^(2)` and `a` of copper `=17xx10^(-6)//K`).

Answer

`Y_(2) = 1.105 xx 10^(11) N//m^(2), alpha_(2) = 2 xx 10^(-5)//.^(@)C`

Explanation

`Deltal = 1.91 mm = Deltal_(1) +Deltal_(2)`
`rArr 0.191 cm = l_(1) alpha_(1) Delta theta +l_(1) alpha_(2) Delta theta`.
`rArr 0.191 = (30 xx 17 xx 10^(-6) +70 alpha_(2)) xx 100`
`alpha_(2) = 2 xx 10^(-5)`
`Y = (F)/(A alpha Delta theta)`
`F_(1) = F_(2)`
`Y_(1)A alpha_(1)Delta theta = Y_(2) A alpha_(2) Delta theta`.
`:. Y_(2) = (Y_(1)alpha_(1))/(alpha_(2)) = (1.3 xx 10^(11) xx 1.7 xx 10^(-5))/(2 xx 10^(-5))`
`= 1.105 xx 10^(11) N//m^(2)`