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Two rods one of aluminium and the ot...

Two rods one of aluminium and the other made of steel having initial length `l_(1)` and `l_(2)` are connected together to form a single rod of length `l_(1) + l_(2)` . The co - efficient of linear expansion for aluminium steel are `a_(a)` and `alpha_(a)` respectively . If the length of each rod increases by ghe same amount when their temeperature are raised by `+ .^(@)C` then find the ratio `(l_(1))/(l_(1)+ l_(2))`

Text Solution

Verified by Experts

As the lengths of the two rods increases by the same amount so
`l_(1) alpha_(a) t = l_(2) alpha_(s) t "(or) " .(l_(2))/(l_(1)) = (alpha_(a))/(alpha_(s)) rArr (l_(2))/(l_(1)) + 1= (alpha_(a))/(alpha_(s)) + 1`
or `(l_(2) + l_(1))/(l_(1)) = (alpha _(s) + alpha_(s))/(alpha_(s))`
`:. , (l_(1))/(l_(2) + l_(1)) = (alpha_(s))/(alpha_(a) + alpha_(s))`
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