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Question -

A rod of length 1.05 m having negligible mass is supported at its ends by two wires of steel (wire A ) and aluminium (wire B) of equal lengths as shown in figure.
The cross-sectional areas of wires A and B are 1.0 mm2 and 2.0 mm_2, respectively. At what point along the rod should a mass m be suspended in order to produce (a) equal stresses and (b) equal strains in both steel and aluminium wires.



Answer -

For steel wire A, l1=l; Az = 1 mm2;Y1= 2 x 1011 Nm-2
For aluminium wire B, l2 = l; A2 = 2mm2;Y2 = 7 x 1010 Nm-2
(a) Let mass m be suspended from the rod at distance x from the end where wireA is connected. Let Fand F2 be the tensionsin two wires and there is equal stress in two wires, then
(b) Let mass m be suspended from the rod at distance x from the endwhere wire A is connected. Let F1 and F2 be thetension in the wires and there is equal strain in the two wires i.e.,

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