Three elastic wires PQ, PR and PS support a body P of mass M, as shown in figure. The wires are of the some material and cross sectional area, the middle one being vertical. Find the loads by each wire.

Three elastic wires PQ, PR and PS support a body P of mass M, as shown

1.	Three elastic wires PQ, PR and PS support a body P of mass M, as shown in figure. The wires are of the some material and cross sectional area, the middle one being vertical. Find the loads by each wire.
Answer» `Mg//1+ 2 cos^(2)THETA` `Mg//1+ 2 cos^(3)theta` `Mg cos^(2)theta//1+ 2cos^(3)theta` `Mg costheta//1+ 2cos^(3)theta` Solution :Figure shows the situationwhentheload (boby P) descends dueto thestretchinload wires. The new positionsof wires PQ andPsare shown by thedotted lines. Let `T_(1), T_(2)` and`T_(3)`be the loads(tensions) carried by the three wires PQ, PR and PS respectivelywith thewires PQ and PS makingangle `theta` with the vertical . Consideringthe horizontal equilibrium ofpointP, `T_(1)sin theta= T_(3) sin rArr T_(1) = T_(3) = T("SAY")` Considering the veritcalequilibrium of point P, `T_(2) +2T cos theta = Mg""......(i)` PR =a `THEREFORE ` PQ = PS = a sec`theta` I f`deltal_(1)` and `deltal_(2)` bethe elongations in thewires PR and PQ (or Ps ) respectively then `deltal_(2) = deltal_(1) cos theta` (from geometry) If A nd Y be the cross- sectional area and Young'smodaulus of reachof the each of the three wires, then `(T)/(AY)(a sectheta) = (T_(2))/(AY ) a cos theta rArr T =T_(2) cos ^(2) theta""....(ii)` Sloving eqns. (i) and (ii) we get `T_(2) = (Mg)/(1+2 cos^(3) theta)`