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Two rods, one of aluminium and the other made of steel, having initial length `l_1 and l_2` are connected together to from a single rod of length `l_1+l_2.` The coefficients of linear expansion for aluminium and steel are `alpha_a and alpha_s` and respectively. If the length of each rod increases by the same amount when their temperature are raised by `t^0C,` 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))`

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Correct Answer - C
(c) The lengths of reach rod increases by the same amount
`:. Deltal_a=Deltal_s`
`rArrl_1alpha_at=l_2alpha_at`
`rArr(l_2)/(l_1)=(alpha_a)/(alpha_s) rArr (l_2)/(l_1)+1=(alpha_a)/(alpha_s)+1`
`rArr(l_2+l_1)/(l_1)=(alpha_a+alpha_s)/(alpha_s) rArr (l_1)/(l_1+l_2)=(alpha_s)/(alpha_a+alpha_s)`

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