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Two rods, one of aluminium and other made of steel, having initial lengths `l_(1) and l_(2)` are connected together to form a single rod of length `(l_(1)+l_(2))`. The coefficient of linear expansions for aluminium and steel are `alpha_(a)` and `alpha_(s)` respectively. If length of each rod increases by same amount when their tempertures are raised by `t^(@)C`, then find the ratio `l_(1) (l_(1)+l_(2))`.

A

`(alpha_(s))/(alpha_(a))`

B

`(alpha_(a))/(alpha_(s))`

C

`(alpha_(s))/(alpha_(a)+ alpha_(s))`

D

`(alpha_(a))/(alpha_(a)+ alpha_(s))`

Text Solution

Verified by Experts

The correct Answer is:
C
As `Delta l_(1) = Delta l_(2) :. Alpha_(a) l_(1) T = alpha_(3) l_(2) T`
or `(l_(2))/(l_(1)) = (alpha_(a))/(alpha_(s)) or (l_(2))/(l_(1)) + 1 = (alpha_(a))/(alpha_(s)) +1 or (l_(2) + l_(1))/(l_(1)) = (alpha_(a) + alpha_(s))/(alpha_(s))`
`:. (l_(1))/(l_(1) + l_(2)) = (alpha_(s))/(alpha_(a) + alpha_(s))`
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