GATE 2025 ME – Question 62
Two metal parts (a cylinder and a cube) of same volume are cast under identical conditions. The diameter of the cylinder is equal to its height. The ratio of the solidification time of the cube to that of the cylinder is________ (rounded off to 2 decimal places).
Assume that solidification time follows Chvorinov's rule with an exponent of 2.
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Correct answer: 0.84 to 0.86
Explanation
By Chvorinov's rule, the solidification time is proportional to $\left(\frac{V}{A}\right)^2$. Take $V = 1$. For the cube, the side is 1 and the surface area is 6, so $\frac{V}{A} = 0.1667$. For the cylinder with $d = h$, the volume gives $d = \left(\frac{4}{\pi}\right)^{1/3} = 1.0839$, and the surface area is $2 \times \frac{\pi d^2}{4} + \pi d \cdot d = 1.5\pi d^2 = 5.536$, so $\frac{V}{A} = 0.1806$. The ratio of the times is $\left(\frac{0.1667}{0.1806}\right)^2 = 0.85$, which is the time of the cube divided by the time of the cylinder.