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Question

# A strip with cross-sectional area 150 mm × 4.5 mm is being rolled with 20% reduction of area using 450 mm diameter rollers. The angle subtended by the deformation zone at the roll centre is (in radians)

A
0.01
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B
0.02
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C
0.03
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D
0.06
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Solution

## The correct option is D 0.06Bite angle: θ=tan−1⎛⎜ ⎜ ⎜⎝√RΔhR−Δh2⎞⎟ ⎟ ⎟⎠ From question, we have 20% reduction in cross-sectional area 150 × 4.5 × 0.8 = 150 × h h=3.6 mm Δh=4.5−3.6=0.9 mm Given,R=4502=225 mm θ=tan−1⎛⎜ ⎜ ⎜⎝√225×0.9225−0.92⎞⎟ ⎟ ⎟⎠ =3.62∘=0.06 rad

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