Question

If a wire has poisons ratio of 0.5 it is stretched by an external force to produce a longitudinal strain of 2 into 10 raise to minus 3 if the original diameter was 2 millimetre the final diameter of the stretching is??​

Answer 1

Given :

Poison’s ratio = 0.5

Longitudinal strain = 2×10⁻³

Diameter of the wire = 2mm

To find :

The final diameter of the wire

Solution :

• We know the relation, Poisons ratio = -ΔR/R / (ΔL/L)

        -ΔR/R = Poisons ratio× (ΔL/L)

                   = 0.5 × 2×10⁻³

                   = 1×10⁻³

• -ΔR = 1×10⁻³× 1

        -ΔR = 1×10⁻³

         R₁ -R₂ = 0.002

         R₂ = 2 - 0.002

         R₂ = 0.998mm

         D₂ = 1.996 mm

The final diameter of the wire is  1.996 mm