An aluminium rod of length `l_(1)` and an iron rod of length `l_(2)` are joined lengthwise to form a single rod of length `(l_(1)+l_(2))`. Coefficients of linear expansion of aluminium and iron are `alpha_(a) " and " alpha_(s)` respectively. If both the rods expand equally for a rise in temperature t find the ratio between `l_(1) " and " (l_(1)+l_(2))`.

Explanation

Expansion of aluminium rod for rise t in temperature `-l_(1)alpha_(a)t`
and that of iron rod for the same rise in temperature `=l_(2)alpha_(s)t.`
According to the problem,
`" "l_(1)alpha_(a)t=l_(2)alpha_(s)t`
`therefore " "l_(1)/l_(2)=alpha_(s)/alpha_(a)`
`therefore " "l_(1)/(l_(1)+l_(2))=alpha_(s)/(alpha_(a)+alpha_(s)).`