The stress along the length of 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 Young's modulus, Y= stress strain = F A l l Y= Y 100 l ( . putting . F A = Y 100 ) l l = 1 100 Poisson's ratio, = - r r l l r r =- l l = -0.3 100 r r = -0.3 100 Change in volume, V V = 2 r r + l l array l = 2 (-0.3) 100 + 1 100 = 1-0.6 100 = 0.4 100 array V %=0.4 %