Three rods of equal l are joined to from an equilateral trangle 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., alpha_(2) but for PQ is alpha_(1^.) Then

Three rods of equal l are joined to from an equilateral trangle PQR.O

1.	Three rods of equal l are joined to from an equilateral trangle 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., alpha_(2) but for PQ is alpha_(1^.) Then
Answer» `alpha_(2) = 3 alpha_(1)` `alpha_(2) = 4 alpha_(1)` `alpha_(1) = 3 alpha_(2)` `alpha_(1) = 4 alpha_(2)` Solution :`(OR)^(2)=(PR)^(2)-(PO)^(2)=L^(2)-(l/2)^(2)` `""=[l(1+alpha_(2)t)]^(2)-[1/2(1+alpha_(l)t)]^(2)` `l-(l^(2))/4=l^(2)(1+alpha_(2)^(2)t^(2)+2alpha_(2)t)-(l^(2))/4(1+alpha_(1)^(2)t^(2)+2alpha_(l)t)` Neglecting `alpha_(2)^(2)t^(2)and alpha_(1)^(2)t^(2)` `""0=l^(2)(2alpha_(2)t^(2))-(l^(2))/4(2alpha_(l)t)` `rArr""2alpha_(2)=(2alpha_(1))/4` `rArr""alpha_(1)=4alpha_(2)`