A compressive force is applied to a uniform rod of rectangular cross-section so that its length decreases by 1 % . If the Poisson's ratio for the material of the rod be 0.2, which of the following statements is correct? "The volume approximately ...........

Step-by-step solution

Given, Decrement in the length =1 % Poisson's ratio for material of the rod, =0.2 As we know that, Volume, v= r² l,[ where , l is the length of the rod ] V V = 2 r r + l l ...(i) since, Poisson's ratio, = - D / D L / L = - r / r L / L So, Eq. (i) can be written as, aligned V V = l l (1-2 ) V V 100 &= ( l l 100 ) (1-2 ) &=-1 [1-2 (0.2)] &=-1 [1-0.4] &=-0.6 % aligned Here, negative sign shows the decrement in the volume.