Engineering
Physics
Stress Strain and Hookes Law New
Question

Two rods of identical dimensions, with Young’s moduli Y1 and Y2 are joined end to end. The equivalent Young’s modulus for the composite rod is

2Y1Y2 / (Y1+Y2)

Y1Y2 / (Y1+ Y2)

1/2 (Y1+Y2)

Y1 + Y2

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Solution

To get Y effective we assume a rod of new material but having same dimension as combind given rod. 

Now use  change in new rod  is equals to sum of  change in two given rods while there are under same stress.

F2l / AY = Fl / AY1 + Fl / Ay2

Y=2Y1Y2 / (Y1+Y2)