The radius of curvature of a railway line at a place when the train is moving with a speed of 36 `kmh^(-1)` is 1000 m, the distance between the two rails being 1.5 metre. Calculate the elevation of the outer rail above the inner rail so that there may be no side pressure on the rails.

Explanation

Velocity, v = 36 km `h^(-1) = (36 xx 1000)/(3600) ms^(-1) = 10 ms^(-1)`
radius, r = 1000m , tan `theta = (v^(2))/(rg)`
= 1000 `xx 9.8 = (1)/(9.8)`
Let h be the height through which outer rail is raised. Let l be the distance between the two rails.
Then, tan `theta = (h)/(l) " " `[ `therefore theta` is very small ]
or h = l tan `theta`
h = 1.5 `xx (1)/(98) m = 0.0153 `m [ `therefore` l = 1.5 m ]