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# Three rods of equal length l are joined to form an equilateral triangle PQR. O is the mid point of PQ. Distance OR remains same for small change in temperature. Coefficient of linear expansion for PR and RQ is same i.e. ${\mathrm{\alpha }}_{2}$ but that for PQ is ${\mathrm{\alpha }}_{1}$. Then

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a
α2=3α1
b
α2=4α1
c
α1=3α2
d
α1=4α2
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detailed solution

Correct option is D

(OR)2=(PR)2−(PO)2=l2−l22l1+α2t2−121+α1t2l2−l24=l21+a22t2+2α2t−l241+a12t2+2α1tNeglecting α22t2 and α12t20=l22α2t−l242α1t⇒2α2=2α14⇒;α1=4α2

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The coefficient of linear expansion of brass and steel are ${\mathrm{\alpha }}_{1}$ and ${\alpha }_{2}$. If we take a brass rod of length ${l}_{1}$ and steel rod of length ${l}_{\mathit{2}}$ at 0oC, their difference in length $\left({l}_{2}-{l}_{1}\right)$will remain the same at all temperatures if

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