The radius of curvature of a railway line at a place when the train is moving with the speed of 36 km per hr is 1000m. The distance between the two rails being 1.5m. Calculate the elevation of outer rail above the inner rail so that there may be no side pressure on the rails

Here,

r = 1000 m

v = 10 m/s

d = 1.5 m

Let α be the angle of elevation of the tracks and x be the elevation of the outer track.

Let side wise pressure of the left wheel be F₁ and F₂ be of the right

Now by FBD

Mg sinα = F₁

(Mv²/r) cosα = F₂

Now to have no sidewise pressure

F₁ = F₂

=> Mg sinα = (Mv²/r)cosα

=> tan α = v²/rg = 10²/(1000 × 9.8) = 0.01

Now we have

x = d tanα = 1.5 × 0.01 = 0.015 m