Question

In a two-stage wire drawing operation, the fractional reduction (ratio of change in cross- sectional area to initial cross-sectional area) in the first stage is 0.4. The fractional reduction in the second stage is 0.3. The overall fractional reduction is

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Solution

The correct option is **B** 0.58

Fractional reduction in first stage =Change in area in first stageOriginal area (A) before reduction

0.4=Change in area in first stageA

Change in area in first stage

=0.4A

Area after first redirection

=A−0.4A=0.6A

Fraction reduction in second stage

=Change in area in second stageOriginal area (A) before second stage

0.3=Change in area in second stage0.6A

Change in after 2nd stage

=0.18A

Remaining area after 2nd reduction

=0.6A−0.18A=0.42A

Overall reduction in area

=A−0.42A=0.58A

Overall fractional reduction

=Overall reduction in areaOriginal area=0.58AA=0.58

Fractional reduction in first stage =Change in area in first stageOriginal area (A) before reduction

0.4=Change in area in first stageA

Change in area in first stage

=0.4A

Area after first redirection

=A−0.4A=0.6A

Fraction reduction in second stage

=Change in area in second stageOriginal area (A) before second stage

0.3=Change in area in second stage0.6A

Change in after 2nd stage

=0.18A

Remaining area after 2nd reduction

=0.6A−0.18A=0.42A

Overall reduction in area

=A−0.42A=0.58A

Overall fractional reduction

=Overall reduction in areaOriginal area=0.58AA=0.58

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