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
(Assume cubical shape of man with $L$ as edge length)

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Solution

We know stress is given by
$Stress = \frac{Force}{Area} = \frac{m g}{A} = \frac{ρ V g}{A} (∴ ρ = \frac{m}{V})$
i.e., stress $\propto \frac{L^{3}}{L^{2}}$ (L is the linear dimension).
$\Rightarrow stress \propto L$
Since linear dimension increases by a factor of 9, stress also increases by a factor of 9.

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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 (Assume cubical shape of man with L as edge length)

We know stress is given by Stress=ForceArea=mgA=ρVgA(∴ρ=mV) i.e., stress ∝L3L2 (L is the linear dimension). ⇒stress ∝L Since linear dimension increases by a factor of 9, stress also increases by a factor of 9.

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
(Assume cubical shape of man with $L$ as edge length)