The Poisson's ratio of a material is 0.1 . If the longitudinal strain of a rod of this material is 10⁻³ , then the percentage change in the volume of the rod will be

Step-by-step solution

If and be the longitudinal strain and lateral strain respectively, then = l₂-l₁ l₁ =10⁻³=0.001 l₂ l₁ =1.001 Poisson's ratio, = Lateral strain Longitudinal strain = array ll & = =0 But, & = r₁-r₂ r₁ array r₁-r₂ n₁ =10⁻⁴=0.0001 r₂ r₁ =0.9999 Hence, percentage increase in vol = V₂-V₁ V₁ 100= r₂² l₂- r₁² l₁ r₁² l₁ 100= [ ( r₂ r₁ )² ( l₂ l₁ )²-1 ] 100= [(0.9999)² (1.0001)²-1 ] 100=0.0008 100=0.08 %