A 4 mm thick sheet is rolled with 300 mm diameter rolls

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A 4 mm thick sheet is rolled with 300 mm diameter rolls to reduce thickness without any change in its width. The friction coefficient at the work-roll interface is 0.1. The minimum possible thickness of the sheet that can be produced in a- single pass is

1. 1.0 mm
2. 1.5 mm
3. 2.5 mm
4. 3.7 mm

Correct Option: C

Given, Initial thickness of sheet, t_i = 4 mm = 4 × 10^–3 m
Diameter of roll, D = 300 mm = 0.3 m
Frictional coefficient at work-roll interface, μ = 0.1
Let t_f = Final thickness of sheet after rolling
For single pass without slipping minimum possible thickness,
t_i - t_f = μ²R
μ = √(t_i - t_f) / R
0.1 = √(4 × 10^–3 - t_f) / 0.15
or t_f = 2.5 mm