First slide

Toppling

Question

A railway track is banked for a speed v, by making the height of the outer rail h higher than that of the inner rail. The distance between the rails is d. The radius of curvature of the track is r

Moderate

A

$\frac{h}{d} = \frac{v^{2}}{r g}$
B

$\tan (\sin^{- 1} \frac{h}{d}) = \frac{v^{2}}{r g}$
C

$\tan^{- 1} (\frac{h}{d}) = \frac{v^{2}}{r g}$
D
$\frac{h}{r} = \frac{v^{2}}{d g}$

Solution

For optimum angle of banking ,
$\frac{m v^{2}}{r} \cos θ = m g \sin θ$ = mg sinθ
$\tan θ = \frac{v^{2}}{r g}$

Here sin θ = h/d

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