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EEJ MAIN Physics QUESTION #7100
Question 1
If a human grows into a giant such that all linear dimensions increase by a factor of $9$ while density remains the same, by what factor does the stress in the leg change? [cite: 457]
  • $\frac{1}{81}$
  • 9✔️
  • $\frac{1}{9}$
  • 81
Correct Answer Explanation

Stress is defined as $\frac{\text{Force}}{\text{Area}}$ [cite: 457].

  • Force (Weight) $W \propto \text{Volume} \times \text{density} \propto L^3$
  • Area $A \propto L^2$
  • $\text{Stress} \propto \frac{L^3}{L^2} \propto L$
  • Since $L$ increases by $9$, the stress increases by a factor of $9$[cite: 457].