Q.

Two rods, one of aluminium and the other made of steel, having initial length  l1 and l2  respectively are  connected together to  form a single rod of length l1+l2 . The coefficient  of linear  expansion for aluminium and steel are  αa and  αs respectively. If the length of each rod  increases by the same amount when their  temperature t0C are raised by  , then  find the ratio  l1l1+2

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a

αsαa

b

αaαs

c

αsαa+αs

d

αaαa+αs

answer is C.

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Detailed Solution

l1α1=l2α2l1l2=α2α1l1l2+1=α2α1+α1l1+l2l2=α1+α2α1l1l1+l2=α2α2+α1
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Two rods, one of aluminium and the other made of steel, having initial length  l1 and l2  respectively are  connected together to  form a single rod of length l1+l2 . The coefficient  of linear  expansion for aluminium and steel are  αa and  αs respectively. If the length of each rod  increases by the same amount when their  temperature t0C are raised by  , then  find the ratio  l1l1+2