A train is moving with a speed of 12 m/s on rails which are 1.5 m apart. To negotiate a curve of radius 400 m, the height by which the outer rail should be raised with respect to the inner rail is (Given, g=10 m/s²)

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(1) 5.4 cm. Idea: for small banking angles the required tilt is tan θ=(v²)/(rg), and the height is that tilt times the gauge: h=ℓ tan θ. tan θ=(v²)/(rg)=(144)/(400×10)=(144)/(4000)=0.036. h=ℓ tan θ=1.5×0.036=0.054 m h=5.4 cm. A tilt of 0.036 is about 2°, so treating sin θ≈tan θ costs nothing — which is why real railway cant is quoted as a height rather than an angle.

A train is moving with a speed of 12 m/s on rails which are 1.5 m apart. To negotiate a curve of radius 400 m, the height by which the outer rail should be raised with respect to the inner rail is (Given, g=10 m/s²)

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