GATE 2024 PI – Question 15
A cube of side a and cylinder of radius r and length 4r, of the same material and sand-casting process, have equal solidification times under Chvorinov’s equation. Find r/a.
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Correct answer: (B) 5/12
Explanation
Equal times imply equal V/A. The cube modulus is a/6. The cylinder has $V=4\pi r^3$ and $A=8\pi r^2+2\pi r^2=10\pi r^2$, so its modulus is 2r/5. Equating $a/6=2r/5$ gives **r/a = 5/12, B**.