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

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 $m = \rho V$, where $\rho$ is the density and $V$ is the volume. Since the man grows geometrically similar, the volume $V$ is proportional to $h^3$. Thus, $m \propto h^3$.

The stress $\sigma$ in the legs is defined as the force per unit area, $\sigma = \dfrac{F}{A} = \dfrac{mg}{A}$.

Since the man grows geometrically similar, the cross-sectional area $A$ of the legs scales as $h^2$.

Substituting the scaling relations $m \propto h^3$ and $A \propto h^2$ into the stress formula, we get $\sigma \propto \dfrac{h^3}{h^2} = h$.

Given that the height increases by a factor of 8, the stress in the legs will also increase by a factor of 8.

Answer: 8