COMEDK · Physics · 10. Mechanical Properties of Solids

A man grows into a giant such that his height increases to 8 times his original height. Assuming that his density remains same, the stress in the leg will change by a factor of

A \(2 \sqrt{2}\)
B 16
C 8
D 4

Verified Solution

Answer & Solution

Correct Answer

(C) 8

Step-by-step Solution

Detailed explanation

Let the original height of the man be \(h\) and the original cross-sectional area of his legs be \(A\). The mass of the man is \(m = \rho V\), where \(\rho\) is the density and \(V\) is the volume. Since the man grows geometrically similar, the volume \(V\) is proportional to…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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