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# Coefficient of linear expansion of brass and steel rods are  ${\alpha }_{1}$and ${\alpha }_{2}$ Lengths of brass and steel rods are ${\mathcal{l}}_{1}$and ${\mathcal{l}}_{2}$respectively. If $\left({\mathcal{l}}_{2}-{\mathcal{l}}_{1}\right)$ is maintained same at all temperatures, which one of the following relations holds good?

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a
α12l2=α22l1
b
α1l1=α2l2
c
α1l2=α2l1
d
α1l22=α2l12

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detailed solution

Correct option is B

Linear expansion of brass =α1 Linear expansion of steel =α2 Length of brass rod =l1 Length of steel rod =l2On increasing the temperature of the rods by ∆T, new lengths would bel1'=l11+α1ΔT........(1)l2'=l21+α2ΔT.........(2) Subtracting eqn. (i) from eqn. (ii), we get l2'-l1'=l2-l1+l2α2-l1α1ΔTAccording to the question l2'-l1'=l2-l1∴l2α2-l1α1=0 or l1α1=l2α2

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