Q 11-08-102JEE MainJEE Main 2017 (2 Apr)Easy
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:
Answer: (B) $9$
Stress in the leg $=\dfrac{\text{weight}}{\text{cross-sectional area}}$.
With the same density, weight $\propto$ volume $\propto L^3$, while area $\propto L^2$. So
$$\text{stress} \propto \frac{L^3}{L^2} = L$$
Increasing $L$ by a factor of $9$ increases the stress by a factor of $9$.
Solution by Sreeraj P, M.Sc Physics