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Question

A light rod AB of length 2 m is suspended from the ceiling horizontally by means of two vertical wires as shown in Fig. One of the wires is made of steel of cross-section 0.1 cm2 and the other of brass of cross-section 0.2 cm2. The Young's modulus of brass is 1.0 ×1011 Nm2 and of steel is 2.0×1011 Nm2. A weight W is hung at point C at a distance x from end A. It is found that the stress in the two wires is the same when x=n3 metre. Find the value of n.



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Solution


Let Ts and Tb be the tension in steel and brass wire.
From the data given in the question,
Stress in steel wire =Stress in brass wire.
TsAs=TbAb TsTb=AsAb=0.1 cm20.2 cm2TsTb=12 ......(1)
The system is in Rotational equilibrium calculating and equating the torque about C.
Ts×n3=Tb(2n3)
TsTb=(2n3)n3
From equation (1)
12=(2n3)n3
n3=2×(2n3)
n3=42n3
n=4

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