GATE 2024 CE (CE1) – Question 62
The number of trains and their corresponding speeds for a curved Broad Gauge section with 437 m radius, are
• 20 trains travel at a speed of 40 km/hr
• 15 trains travel at a speed of 50 km/hr
• 12 trains travel at a speed of 60 km/hr
• 8 trains travel at a speed of 70 km/hr
• 3 trains travel at a speed of 80 km/hr
If the gauge (center-to-center distance between the rail heads) is taken as 1750 mm, the required equilibrium cant (in mm) will be ______________ (rounded off to the nearest integer).
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Correct answer: 88
Explanation
The equilibrium speed is taken as the weighted average speed: $V = \frac{20 \times 40 + 15 \times 50 + 12 \times 60 + 8 \times 70 + 3 \times 80}{58} = \frac{3070}{58} = 52.93$ km/h. The equilibrium cant is $e = \frac{GV^2}{127R} = \frac{1750 \times 52.93^2}{127 \times 437} = 88.3$ mm, which is 88 mm.