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in Physics by (69.2k points)

Two metal wires A and B have the same length l under no loading.

The Young’s moduli are YA and YB , cross-sectional areas are α and 2 α for A and B respectively. The rod PQ is light. Now a load W is applied.

(a) Write extension in the wires A and B as a function of x.

(b) Write the value of x for equal stress in the wires.

(c) Write the value of x for equal strain in the wires.

1 Answer

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Best answer

Let tension be TA in A and TB in B.The equilibrium of rod suggests that moment of wand TB about P must be balanced. Hence

The stress in the wire A is given by

The stress in the wire Bis given by

(b) Equal stresses in the two wires means

Putting the values of TA and TB ,

(c) Equal strains in the two wires means

Putting the values of TA and TB ,

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