GATE 2026 PI – Question 45
A 10 cm steel cube is sand cast using a cylindrical side riser of diameter d and height h. Assume no shared cooling surface between casting and riser; d = h; the connecting link does not freeze before the casting; and all surfaces have identical cooling conditions. Which ONE OR MORE d values (cm) can theoretically fully compensate casting shrinkage?
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Correct answer: (C) 15; (D) 20
Explanation
For the cube, casting modulus is $M_c=V/A=10^3/[6(10^2)]=5/3$ cm. For a cylinder with h = d and all surfaces cooling, $M_r=(\pi d^3/4)/(3\pi d^2/2)=d/6$. To remain liquid longer under Chvorinov’s law, $M_r>M_c$, requiring d > 10 cm. Therefore **15 and 20 cm: C,D**. This is the theoretical thermal criterion intended by the problem.