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Q.

Two uniform metal rods one of aluminium of length l1 and another made of steel of length l2 and linear coefficients of expansion αa and αs respectively are connected to form a single rod of length l1+l2 . When the temperature of the combined rod is raised by t°C, the length of each rod increases by the same amount. Then l1l1+l2 is

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a

αsαa+αs

b

αaαa+αs

c

αaαs

d

αsαa

answer is A.

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Detailed Solution

l1αaΔt1=l2αsΔt2
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Two uniform metal rods one of aluminium of length l1 and another made of steel of length l2 and linear coefficients of expansion αa and αs respectively are connected to form a single rod of length l1+l2 . When the temperature of the combined rod is raised by t°C, the length of each rod increases by the same amount. Then l1l1+l2 is