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GATE 2019 CE (CE1) – Question 21

Transportation Infrastructure · Geometric design of roadways: cross-section, sight distance, alignments · 1 mark · Multiple choice

The average coefficient of rolling friction of a road is $f_r$ and its grade is +G%. If the grade doubles with other parameters unchanged, find the percentage change in horizontal braking distance.

  1. $\frac{0.01G}{f_r+0.02G}\times100$
  2. $\frac{f_r}{f_r+0.02G}\times100$
  3. $\frac{0.02G}{f_r+0.01G}\times100$
  4. $\frac{2f_r}{f_r+0.01G}\times100$

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Correct answer: (A) $\frac{0.01G}{f_r+0.02G}\times100$

Explanation

Braking distance on an uphill grade is proportional to $1/(f_r+0.01G)$. After doubling the grade, the distance ratio is $(f_r+0.01G)/(f_r+0.02G)$. Thus percentage reduction is $$\left[1-\frac{f_r+0.01G}{f_r+0.02G}\right]100=\frac{0.01G}{f_r+0.02G}100.$$ Answer **A**; the listed positive expression is the magnitude of the decrease.