Question

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

• A. $81$
• B. $\frac{1}{81}$
• C. $9$
• D. $\frac{1}{9}$

Answer 1

Answer: (C)

$9$

$\begin{array}{cc}\text{Stress}& =\frac{\text{Force}}{\text{Area}}=\frac{\left(\text{height}\right)\times \text{Area}\times \text{density}\times g}{\text{Area}}\\ & =\text{(height)}(g\times \text{density})\end{array}$

$\begin{array}{c}\text{Stress a height}\\ \text{So stress in leg will also change by a factor of}9.\end{array}$