A train is moving with a speed of 12 m s - 1 on rails which are 1 . 5 m apart. To negotiate a curve radius 400 m , the height by which the outer rail should be raised with respect to the inner rail is (Given, g = 10 m s - 2 ):

Step-by-step solution

For the train, moving along the curved rails, it can be written, with reference to the figure below, that tan θ = v 2 R g . . . 1 Also, from the above figure, it follows that tan θ = h 1 . 5 . . . 2 Equations (1) and (2) imply that h 1 . 5 = v 2 R g ⇒ h = 1 . 5 × v 2 R g = 1 . 5 × 12 m s - 1 2 400 m × 10 m s - 2 = 0 . 054 m = 5 . 4 cm