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GATE 2021 AG – Question 42

Soil and Water Conservation Engineering · Soil and Water Erosion · 2 marks · Multiple choice

Bench terraces are planned on10% land slope, vertical interval2.5 m, batter slope100%. Find working width(m) and cultivated-area loss(%).

  1. 22.50 and .05
  2. 25.00 and .50
  3. 22.50 and 10.45
  4. 25.00 and 10.45

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Correct answer: (C) 22.50 and 10.45

Explanation

Horizontal terrace interval is 2.5/.10=25 m. The1:1 batter occupies2.5 m horizontally, leaving working width22.5 m. Original sloping ground length per interval is $25\sqrt{1+.10^2}=25.12469$ m. Area lost relative to that original surface is $(25.12469-22.5)/25.12469\times100=10.44665\%$. Thus **22.50 m and 10.45%,C**. Accounting for original ground slope explains why loss slightly exceeds the10% horizontal projection.

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