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
B
9
C
19
D
81

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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