In a slush casting process, a casting of thickness 5 mm is formed when the mold is invert after 100 seconds and a thickness of 7 mm is formed when the mold is inverted after 200 seconds. What is the time after which the mold has to be inverted to produce the thickness of casting as 2 mm?

2.5 sec

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20 sec

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40 sec

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6.25 sec

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Solution

The correct option is D 6.25 sec
$t_{1} = 5 m m, T_{1} = 100 s e c t_{2} = 7 m m, T_{2} = 200 s e c t_{3} = 2 m m, T_{3} = ? t_{1} = C_{1} \sqrt{T_{1}} + C_{2} t_{2} = C_{1} \sqrt{T_{2}} + C_{2} 5 = C_{1} \sqrt{100} + C_{2} - - - - (1) 7 = C_{1} \sqrt{200} + C_{2} - - - - (2)$

From equation. (1) & (2)

$C_{1} = 0.4828, C_{2} = 0.1715 t_{3} = C_{1} \sqrt{T_{3}} + C_{2} 2 m m = 0.4828 \sqrt{T_{3}} + 0.1715 \Rightarrow T_{3} = 6.25 s e c$

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200 \times 100 \times 60

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