The longitudinal stress in a rod (with rectangular cross-section) is 1 % of the Young's modulus of its material. What is the approximate percentage of change of its volume? (Poisson's ratio of the material of the rod is 0 . 3 )

Step-by-step solution

∵   Stress, F ∆ A = 1 % of Y = Y 100 But Y o u n g ′ s modulus, Y = s t r e s s s t r a i n = F ∆ A ∆ l l ∴       Y = Y 100 ∆ l l             p u t t i n g F ∆ A = Y 100 ∴     ∆ l l = 1 100 P o i s s o n ′ s ratio, σ = - ∆ r r ∆ l l ∴     ∆ r r = - σ ⋅ ∆ l l = - 0.3 100 ∆ r r = - 0.3 100 ∴     Change in volume, &#8