A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains the same, the stress in the leg will change by a factor of

Question

Accepted Answer

(1) 9. The stress in the leg is the weight carried divided by the cross-sectional area of the bone. At fixed density the mass follows the volume, so the weight scales as L³ and grows by 9³=729. A cross-section is an area, so it scales as L² and grows by 9²=81. Stress ∝(L³)/(L²)=L, so it changes by the factor 9. This is why giant creatures are not just scaled-up people: the stress in the bones rises in proportion to size.

A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains the same, the stress in the leg will change by a factor of

Step-by-step solution

Why the other options are wrong