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

Correct answer: 9

Solution

When the linear dimensions of an object increase by a factor of 9, its volume increases by a factor of 9³ (729), while the weight increases proportionally to the volume. Since stress is defined as force (weight) per unit area, and the area increases by a factor of 9² (81), the stress in the leg will increase by a factor of 9.

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