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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

1. 81
2. 1/81
3. 9
4. 1/9

Correct answer: 9

Solution

When the linear dimensions increase by a factor of 9, the volume increases by a factor of 9³ (729), and since density remains constant, the mass also increases by the same factor. Stress is defined as force per unit area, and since the area increases by a factor of 9² (81), the stress in the leg changes by a factor of 9.

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