A man grows into a giant such that his height increases to 8 times his original height. Assuming that his density remains same, the stress in the leg will change by a factor of

Step-by-step solution

Let the original height of the man be h and the original cross-sectional area of his legs be A . The mass of the man is m = V , where is the density and V is the volume. Since the man grows geometrically similar, the volume V is proportional to h^3 . Thus, m h^3 . The stress in the legs is defined as the force per unit area, = F A = mg A . Since the man grows geometrically similar, the cross-sectional area A of the legs scales as h^2 . Substituting the scaling relations m h^3 and A h^2 into the stress formula, we g