An iron rod and a copper rod lie side by side. As the temperature is changed, the difference in the lengths of the rods remains constant at a value of `10cm` . Find the lengths at `0^(@)C` . Coefficient of linear expansion of iron and copper are `1.1xx10^(-5)//^(@)C` and `1.7xx10^(-5)//^(@)C` respectively.

Explanation

Given `alpha_(i)=1.1xx10^(-5)//^(@)C` , `alpha_(c)=1.7xx10^(-5)//^(@)C`
`(l theta)_(i) : "length of iron rod at" 0^(@)C`
`(l theta)_(c)` : length of copper rod at `0^(@)C`
`(l theta)_(i)` : length of iron rod at `theta^(@)C`
`(l theta)_(c)` : length of copper rod at `theta^(@)C`
`(l_(0))_(i)-(l_(0))_(c)=10`
`(Deltal)_(i)=(Deltal)_(c)`
`(l_(0))_(i)alpha_(i)(theta-0)=(l_(0))=(l_(0))_(c)alpha_(c)(theta-0)`
`(l_(0))_(i)=(l_(0))_(c)alpha_(c)`
`(l_(0))_(i)=(l_(0))_(c)(alpha_(c))/(alpha_(i))=(l_(0))_(c)=(l_(0))_(c)((1.7))/((1.1))` in (i)
`(1.7)/(1.1)(l_(0))_(c)-(l_(0))_(c)=10`
`0.6(l_(0))_(c)=11`
`(l_(0))_(c)=18.3cm`
`(l_(0))_(i)=10+(l_(0))_(c)=28.3cm`