Attempt any THREE :
A meter gauge train is moving at 72 km/hr along a curved rail-way of radius of curvature 500m at a certain place. Find the elevation of the outer rail above the inner rail so that there is no side pressure on the rail. `(g = 9.8 m//s^(2))`

Explanation

Given : `V = 72` km/hr `= (72 xx 1000)/(60 xx 60) = 20` m/s
`l = 1` m , r = 500 m.
As we know , `tan theta = (V^(2))/(rg)`
`tan theta = ((20)^(2))/(500 xx 9.8)`
`tan theta = (400)/(500 xx 9.8) = 4/(49)`
`= 0.0816`
`:. theta = tan^(-1) (0.0816)`
`:. theta = 4^(@) 66'`
Elevation of outer rail above inner rail.
`h = l = sin theta`
`h = (1) sin 4^(@) 66'`
`h = 0.08124 m`