First slide

Banking of road

Question

A train has to negotiate a curve of radius 800 m. By how much height should the outer rail be raised with respect to inner rail for a speed of 96 kmh^-1? The distance between the rails is 1 m.

Moderate

A

4.4 cm
B

9 cm
C

8.9cm
D

3.3 cm

Solution

Given, $v = 96 {kmh}^{- 1} = 96 \times \frac{5}{18} {ms}^{- 1} = 26.67 {ms}^{- 1}$
$∴ \tan θ = \frac{v^{2}}{R g} = \frac{(26.67)^{2}}{800 \times 10} = 0.089$
$\Rightarrow 0.089 = \frac{h}{1} ∴ h = 0.089 m = 8.9 cm$

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