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. α2 but that for PQ is α1. Then

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α2=3α1

α2=4α1

α1=3α2

α1=4α2

answer is D.

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Detailed Solution

(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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