Stress Equality in Supporting Rods

Steps:

• Assume each identical floor has weight $W$; total weight is $4W$.
• Bottom rods (ground to first floor) support all $4W$; top rods (third to fourth floor) support $W$.
• Stress $\sigma = F / A$ is equal in all rods, so cross-sectional area $A \propto F$.
• Since $A = \pi d^2 / 4$, diameter $d \propto \sqrt{F}$; ratio .

Why A is correct:

• Equal stress requires diameters proportional to square root of supported loads, per $\sigma = F / A$.

Why the others are wrong:

• B: Assumes diameters proportional to force (ignores square root), yielding 4.
• C: Overestimates by factor of $\sqrt{8}$, not matching load ratio.
• D: Overestimates by factor of 4, irrelevant to stress formula.

Final answer: A