GATE 2026 MT – Question 58
A 50 mm flat aluminium plate is reduced in thickness to 25 mm in a single pass cold-rolling operation with the rolling diameter of 1250 mm. For this case, the minimum required coefficient of friction between the plate and the roll (rounded off to two decimal places) is ___________.
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Correct answer: 0.19 to 0.21
Explanation
The reduction in thickness is $\Delta h=50-25=25\ \mathrm{mm}$, and the roll radius is $R=1250/2=625\ \mathrm{mm}$. The usual small-angle bite condition is $\Delta h\le\mu^2R$.
Therefore $\mu_{min}=\sqrt{25/625}=0.20$. Enter **0.20**. The roll radius, rather than its diameter, belongs in this expression.