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Question:

A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains the same, the stress in the leg will change by a factor of:

19

181

9

81

Solution:

Stress = force/Area
Let linear dimensions be l, b, h.
Stress = Force/(l × b)
Now, dimensions increase by a factor of 9.
So, Now S' = Force/(9l × 9b) = m*a/(81lb)
S' = ρVa/(81 × lb) ∴ S'/S = 9³V/(81 × lb) × (lb/V)
S' = 9S
Hence stress in leg will change by a factor of 9