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Q.
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 :
JEE MainJEE Main 2017Mechanical Properties of Solids
Solution:
$\frac{v_{f}}{v_{i}}=9^{3}$
$\because$ Density remains same
So, mass $\propto$ Volume
$\frac{m_{f}}{m_{i}}=9^{3}$
$\frac{(\text { Area }) f}{(\text { Area })_{i}}=9^{2}$
Stress $=\frac{(\text { Mass }) \times g}{\text { Area }}$
$\frac{\sigma_{2}}{\sigma_{1}} =\left(\frac{m_{f}}{m_{i}}\right)\left(\frac{A_{i}}{A_{f}}\right)$
$=\frac{9^{3}}{9^{2}}=9$