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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 same, the stress in the leg will change by a factor of :


A
181
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B
9
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C
19
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D
81
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Solution

The correct option is D $$9$$
$$Stress =\dfrac{force}{Area}$$

Let linear dimensions be $$l, b, h$$.

$$Stress = \dfrac{Force}{l\times b}$$

Now, dimensions increase by facror of g.

So, Now $$S'= \dfrac{Force}{9l\times 9b}=\dfrac{ma}{81 lb}$$

$$S' = \dfrac{\rho Va}{81\times lb}$$

$$ \therefore$$ $$\dfrac{S'}{S} = \dfrac{9^3V}{81\times lb}\times \dfrac{lb}{V}$$

$$S'=9S$$
Hence stress in leg will change by factor of $$9$$




Physics

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