JEE Main · 2017 · 02 Apr 2017 · Offline · Elasticity & SHM

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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:

(A)81
(B) $\frac{1}{81}$
(C)9✓ Correct
(D) $\frac{1}{9}$

Answer: (C)

Solution

Stress in the legs is weight divided by cross-sectional area. Scale every length by

9

: the mass, and hence the weight, grows as the volume, a factor

9^{3}

, while the leg's cross-section grows as an area, a factor

9^{2}

. The stress therefore scales as

\frac{9 ^{3}}{9 ^{2}} = 9

, increasing ninefold.

JEE Main · 2017 · 02 Apr 2017 · Offline · Single correct option

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