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in Physics by (49.4k points)

A train is moving round a curve of 52m radius and the distance between the rails is 1.2 m by how much should the outer rails be raised above the inner one so that a train running at the rate of 45 kmhr-1 may not skid.

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Best answer

The angle of banking is given by,

tan θ = \(\frac {v^2}{rg}\)

Here, v = \(\frac{ 45000}{60 \times60}\) 

= 12.5 ms-1 and

r = 52 m 

∴ tanθ = \(\frac{ (12.5)^2}{52\times 9.8}\) 

= 0.3066

θ = tan-1 (0.3066)

= 17°2’

If ‘h’ is the height of the outer rail above the inner one, then 

= 1.2'sin 17.05°

= 0.352 m.

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