Question

# A train has to negotiate a curve of radius$400m$. By how much should the outer rail be raised with respect to the inner rail for a speed of$48km/h$. The distance between the rail is $1m$.

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Solution

## When a vehicle tends to make a turn along a curved road, there is a probability of skidding.The banking of a road is done to provide that centripetal force for the safe turn.The turn is made inclined with the horizontal such that the outer edge is lifted up.Step 1: Given dataRadius of curve (R) = $400m$Width = $1m$Speed (v) = $48km/h=48×\frac{5}{18}m/s=\frac{40}{3}m/s$$g=9.8m}{{s}^{2}}$Let the angle of banking be $\theta$.Step 2: Formula used and calculation of heightWe know that for the banking angle$\theta$.$\mathrm{tan}\theta =\frac{{v}^{2}}{Rg}$, where $g$is the acceleration due to gravity.$\frac{h}{1}=\frac{{v}^{2}}{Rg}\phantom{\rule{0ex}{0ex}}⇒h=\frac{40×40}{3×3}×\frac{1}{400×9.8}\phantom{\rule{0ex}{0ex}}⇒h=0.0453mor4.53cm$Hence, the outer rail must be raised to $0.0453mor4.53cm$.

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