A light rod of length L is suspended from a support horizontally by means of two vertical wires A and B of equal length as shown in Fig. The cross sectional area of A is half that of B and the Young's modulus of A is twice that of B. A weight W is hung as shown. The value of x so that W produces equal stress in wires A and B is-----L3

Let TA and TB be the tensions in wires A and B respectively. If aA and aB are the respective cross-sectional  areas, thenStress in wire A=TAaAStress in wire B=TBaBThe stress in wires A and B will be equal ifTAaA=TBaB or TATB=aAaB=12 (given). Since the system is in equilibrium, the moments of forces TA and TB about C will be equal (see Fig), i.e.TA×x=TB×(L−x)TATB=L−xx  or  12=L−xxwhich gives x=2L3.