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

Answer 1

The correct option is B $9$

$Stress=\frac{Force}{Area}$

Let linear dimensions be $l,b,h$.

$S=\frac{Force}{l\times b}=\frac{\rho Va}{l\times b}$

Now, dimensions increase by factor of $g$.

$S^{\prime }=\frac{Force}{9l\times 9b}=\frac{ma}{81lb}$

$S^{\prime }=\frac{\rho V^{\prime }a}{81\times lb}=\frac{\rho \left(9^{3}V\right)a}{81\times lb}$

$\therefore$ $\frac{S^{\prime }}{S}=\frac{9^{3}V}{81\times lb}\times \frac{lb}{V}$

$S^{\prime }=9S$

Hence, stress in leg will change by a factor of $9$