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.

Explanation

Figure shows the situation wn the load (body `P`) desceneds due to the stretch in the wires. The new positions of wires `PQ` and `PS` are shown by the dotted lines. Let `T_(1)` and `T_(2), T_(3)` be teloads (tensions) carried by the three wires `PQ, PR` and `PS`, respectively, with the wires `PQ` and `PS` making angle `theta` with the vertical.

Considering the horizontal equilibrium of point `P`
`T_(1)sintheta=T_(3)sinthetaimpliesT_(1)=T_(3)=T` (say)
Considering vertical equilibrium of point `P`
`T_(2)+2Tcostheta=Mg`..........i
If `delta_(1)` and `delta_(2)` be the elongations in the wires `PR` and `PQ` (or `PS`), respectively then
`deltal_(2)=deltal_(1)costheta` (from geometry)
If `A` and `Y` be the cross sectional area and Young's modulus of each of the wires, then
`T/(AY)(Asectheta)=(T_(2))/(AY)Acosthetaimplies T=T_(2)cos^(2)theta`........ii
Solving eqn i and ii `T_(2)=(Mg)/(1+2cos^(3)theta)`
and `T_(1)=T_(3)=T=(Mgcos^(2)theta)/(1+2cos^(3)theta)`